There aren't any.
All the so-called "studies" that were done that anti-gay people use, like what Starfish quoted, are studies done against SINGLE-PARENT families to mother-father families. From what I understand, the few studies done against gay parents to non-gay parents indicate that there's NO DIFFERENCE! On the topic of that argument, I grew up with my mother, only seeing my father every two weeks ever since I was seven. I got through puberty just fine ON MY OWN! Whenever my dad tried to explain what was happening to me, I pretty much ignored him. And because I now have to discipline myself (not easy), I will hopefully become stronger in the process.
As to the population argument... that's just ridiculous. I think we can go through about 100 generations before we have to worry about population decline. I'd in fact argue that contraceptives will contribute more to a population decline than homosexual marriage. But again, a population decline is a good thing, at this point. Otherwise we'll just overcrowd the planet, and we haven't even sent a man to mars yet.