i also believe in lovey dovey cartman! not just cause of his established obsession with kyle but because he's already been shown to be lovey dovey with his other partners (heidi, yentl...) but i think EXACTLY because it is kyle that it wouldn't be just limited to over the top affection (or else the relationship wouldn't work on the long term).
the thing with cartman imo is that he deeply believes himself to be unloveable and so when he finds someone that's willing to give him a chance, he represses himself/his personality so as to present himself as someone worth loving. with kyle, well, kyle has already seen the worst of it. he can't fool kyle, kyle knows the real cartman. so in a way i think that would work to their advantage. there's no need for pretending from either side. they can be simultaneously loving and honest to each other. and truly, i don't think they're capable of holding back the genuine irritation they draw out of the other, it's part of the attraction hahah