I have not seen Good Behavior but from what you are saying, it sounds like it encapsulates a good relationship for the two. Might watch a few episodes or binge it if its good haha but I'll come back with more thoughts after that.
In the 90s, the relationship seemed all about tension and it was unique for them. More than the standard 'will they/ won't they' style because there had to be a degree of masochism from both parties and a degree of sadism. They ended up almost taunting each other with happiness and then one or the other would lose it in a moment of weakness. Admittedly, that isn't sustainable story telling for 3 decades but it did work for a time because the audience and the characters got the occasional pay off. The pay off almost always (to my hazy memory) seemed to be punished immediately but people do like the tragic love stories.
Now, in a very serious way, Rogue is the crux of the problem. A 'happy ending' will almost always imply children ever after and, with the scope of Rogue's power, that becomes a hard narrative hurdle. Maybe having her decide to pull a Remy and ask Sinister remove a part of her brain to make her abilities more manageable. Healing factors would need to be addressed but I do like the idea of Rogue getting the idea from a time the Gambit opened up to her and it would give Remy another reason to mistrust Sinister.
We could then also get a Remy/Rogue clone that is the best of both and is, inevitably, a villain (from the future) and the X-Men must defeat them.
Well, that took a turn >.>
The major change that I would make would be that they would start being strong for each other. When Rogue is going defeatist mode because she can't touch without a power inhibitor, Gambit would do more than say sweet nothings, he would blow her self made cage to pieces because he is still happy with her. When Gambit is feeling that self loathing martyrdom/ hero complex out of punishment, Rogue would be there to remind Gambit that he has changed and become better and can continue to grow, that he has friends ( who did we decide on? Laura, Storm, and uhhh Sinister?), that the X-Family wouldn't be the same without a little Cajun.
They would eventually stop sniping at each other in moments of weakness and realize that one can weather the storm for the both of them. That way, they could keep the banter but without the 'hitting below the belt' subtext that we get now.