hard question.....in my heart i think it would have to come from kyle because he's the one who would be most reluctant to the idea of cartman and him being in a relationship. considering cartman has toyed with the idea for his own benefit (tonsil trouble/cartman finds love) i think any resistance, if at all, would be easy to overcome. but kyle, kyle, kyle.........he would have an existential crisis over it. just the idea of realizing he has feelings for cartman would put his world upside down. he might need therapy for that alone. but acting on those feelings???? that's a whole other ballpark
so the world needs to push him to it, imo. a situation where both of their lives are endangered would make him snap out of his denial because he doesnt want to die without having lived his truth (being in love with cartman). alternatively, cartman's life being in danger also would be good because it would dawn on kyle so hard, that he doesnt want to exist without his fatass. that he wants to be with him, that cartman completes him and the threat of cartman being gone is setting off the alarms in his brain
jealousy is also a good one to make the possessive beast in kyle react...i think generally anything that poses a threat to his coexistence with cartman could be an effective trigger for kyle to finally want to claim cartman for himself
im doing the equivalence of kyle confessing = kyman dating because, again, i really think he has the upper hand when it comes to an eventual relationship...and i dont think there'd be a big gap between proclaiming his love and getting together. kyle is gonna take SO LONG to shout his feelings. but when he does then hes gonna assume the consequences, even if its the last thing he does. cartman is something kyle has never fucked around about.