Miss Martian and Superboy are members of the Team who are in a serious relationship with a rocky history. Although they originally wished to keep their relationship a secret, all the other members of the Team and Justice League, eventually found out. Despite the happiness and the stability of their relationship, Superboy broke up with Miss Martian because she attempted to abuse her powers on him. They eventually reconciled and two years later, Superboy proposed to Miss Martian and they are now engaged to be married.
Superboy, just released from Cadmus three days prior, was introduced to Miss Martian on July 8, at the formation of the Team. She took an instant liking to him, and with the knowledge that they would both be living in the Cave, suggested they'd pick adjacent bedrooms. He went for a closet hardly big enough for the two of them.
Initially, they did not get off to a good start, but this was mostly because both were practically aliens unfamiliar with how to live on Earth. Superboy did not appreciate Miss Martian telepathically conversing with him, and lashed out against her for it. The Team had to tell both that that was not normal human behavior. Miss Martian apologized for the invasion of privacy, but Superboy was not as quick on his apologies.
Both were the subject of attention from other teammates. Kid Flash liked Miss Martian, and new member Artemis made no attempt to hide her attraction to Superboy.
Kid Flash's attempts to get M'gann to like him were, as Robin put it, both not very subtle and downright creepy. His actions to impress her annoyed others, especially Artemis, because during a mission to the Tower of Fate, his lies nearly got the Team killed.
Artemis, on the other hand, liked Superboy (at least in appearance) since she first saw him, even before she joined the Team. She witnessed the fight between Superboy and Amazo at the Gotham Academy, and followed him. During her first mission with the Team, she was openly interested in the young boy, which unnerved Superboy, and disgusted Miss Martian. She shrugged off the dismissive comments on her behavior.
Towards a relationship
Miss Martian and Superboy had some close moments together, as they spent quite a lot of time in the Cave with Red Tornado only sporadically checking in. The attraction was obvious to the trained eye; even Clayface noticed it and used it to take them down: Miss Martian was thrilled when "Superboy" called her "gorgeous".
M'gann liked making him dinner, and on one occasion asked for his help. He wanted to help, but Miss Martian's excitement caused him to be covered in the ingredients. She cleaned him up, and they stared at each other for a while, but nothing apparently came of it.
Superboy learned about Miss Martian's true appearance during a mission to Bialya. Their minds had been wiped by Psimon, and when Miss Martian linked their minds to restore it, he caught a glimpse of her white Martian look. He decided not to tell her, as it didn't matter to him, and because he believed she should be allowed to reveal the truth when she was ready. After Psimon was defeated, they almost kissed, but Sphere interrupted them. A semi-kiss would take place, days later, though neither truly considered it their first kiss. During a trip to Atlantis, Ocean-Master destroyed Superboy's rebreather. In the midst of battle, Miss Martian had to lock their lips, and feed him the oxygen she breathed in through her gills. Superboy was eventually given a new rebreather.
As they prepared for school, Aqualad instructed them to take Earth names. M'gann had already thought of hers, and also gave Superboy one: Conner. It was her favorite name, taken from the Hello, Megan! TV show she identified with.
At school, it was obvious to some, like Karen Beecher, that they were an item. M'gann certainly felt that way when, after she was wet from her induction into the Bumblebees, he offered to carry her books. He only saw the practical reason, keeping them dry.
They were sent on a mission in Belle Reve together, disguised as the Terror Twins. During an attempted breakout, Miss Martian was put on ice by Killer Frost. After defeating her and her ally Devastation (with the unwitting help of Icicle Jr.), Superboy found her frozen in ice. At his urging, she used her telekinesis to escape. Overwhelmed by their emotions, they kissed. Their relationship was stable, though Miss Martian accused him of being too protective at times. He eventually apologized, stating he was just worried for her.
The secret relationship
 It didn't last long; by October 1st, just over two weeks after the kiss, Robin and Aqualad had already figured it out. Aqualad had seen it coming and felt no need to tell either Artemis nor Kid Flash.
Zatanna picked it up easily too. She came over for a Halloween party, and noticed the attraction when M'gann worked on Conner's costume. She let it slip to Artemis, whose mood was ruined, as she still considered Conner an option.
Wally was still unaware, and still trying to get together with M'gann. This annoyed both Superboy and Artemis. During Wally's surprise birthday party, while he was desperately trying to score a kiss from M'gann, Artemis told him. He was bummed out.
The Light had discovered M'gann's true appearance, and Queen Bee blackmailed her with it. Though she told the Team her usual appearance wasn't her normal look, she lied again by claiming to be a Green Martian. She also came clean about modeling her life—and by extension, Conner's—on Hello, Megan!. He didn't mind; he also knew she wasn't telling the truth. After Superboy and Artemis told the Team about their true heritage, Miss Martian decided it was time to show them hers. She was afraid of rejection, though Superboy told her he had always known. This, and Aqualad's reaction, gave her confidence a boost. Their relationship survived this small dent, and they became more open with it, also to the League.
The relationship ended shortly before December 1, 2015, when Superboy broke it off. M'gann had tried to psychically alter some of Conner's memories. He caught her and she backed off, though she had the power to push on. She apologized, but Conner felt it went too far. Superboy did not approve of the way Miss Martian used her powers; in his eyes, she abused them. He objected especially to that as her "touch" in his mind had been precious to him, and with this attempt, she had perverted it in his eyes. He had more or less forgiven her, but she did not take it that way. They maintained a working relationship in the Team; both considered themselves professional enough not to let their history obstruct their work.
Eventually, Miss Martian came to realize the error of her ways on how she had been abusing her powers as well as realizing she hadn't been fair to Lagoon Boy, acknowledging him as her rebound boyfriend and broke off the relationship. On June 20, M'gann apologized to Conner and took full responsibility for what she had done, greatly mending their relationship. Everyone around them thought they were getting better, until a mission to Mars where it all fell apart again. Superboy had grown scared of getting close to her again after what had happened.
During a mission to locate Psimon, the villain trapped Miss Martian, Superboy, Beast Boy and Sandra Stanyon inside M'gann's mind. M'gann believed herself to be the character Megan Wheeler from Hello, Megan! and they were all re-enacting an old episode. "Megan" was worried "Conner" wouldn't like the song she was to sing at a talent show, and that he wouldn't forgive her. Forgiveness was the key to get M'gann's mind back in order and get out. Both sides felt they had to forgive the other.
After learning the true reason for the breakup, Gar agreed she went too far, and that Conner didn't have to forgive her. If he did, it has to be earnest: as both a telepath and a girlfriend of five years, M'gann would be able to tell if he was insincere. M'gann dealt with her forgiveness in a different way; she sang a deeply heartfelt and heavy song, expressing how much she regretted damaging her relationship with Conner and admitting she still loved him. After hearing the apology, Conner forgave her for everything. He confessed his enduring love for her and also apologized for his recent distant behavior.
With their relationship fully reconciled and truly restored, M'gann, Conner, Garfield and Sandra are finally set free from M'gann's mind.
After sorting out their relationship, it grew back to being strong and stable over the next two years. Miss Martian and Superboy moved into together in Happy Harbor and acquired jobs as a motorcycle mechanic and student counselor respectively. They found Happy Harbor to be their own Fortress of Solitude, allowing themselves to be together and away from their heroic duties and responsibilities. They were calm and happy together and on July 29, Conner proposed to her and M'gann happily accepted.