There are some champions that can lane against 
Namely

Cho'Gath is the best as he does almost the same thing as Nunu, but better. He can outpush Nunu, and his passive gives him enough sustain to compete with Nunu. If Nunu ever happens to ult, Cho'Gath can easily cancel it with his Rupture or his silence. Stacking magic resistance will also be innefective against the true damage of his Feast. EDIT: Oh, Cho'Gath can also use his Feast to contest objectives, just like Nunu can use his Consume, but Cho'Gath's Feast is better at taking Dragon and Baron due to its higher base damage, but Nunu's Consume has a way lower cooldown. Regardless, Cho'Gath can also beat Nunu at the "objective contest" part.
Mordekaiser also works, mainly due to his passive, which is a shield that allows him to take iceballs a lot better. He can also outpush Nunu, and after a Hextech Revolver, can outsustain him too. There are two problems, though. First, Mordekaiser will hardly be able to kill Nunu late game. Even if he outtrades, Nunu will simply Iceball him and flee. Second, Mordekaiser can't interrupt Nunu's ult.
Vladimir is there too, he will have to play safe but he can survive the lane phase against Nunu instead of being utterly beaten. After a Hextech Revolver, Nunu should not be able to do anything against Vlad. You can outsustain him, outpush him, and even if Vlad can't interrupt Nunu's ult, he can use his pool to avoid any damage, you have to time it properly however.
Other champions that I think that could be able to lane against Nunu but I've yet to test it to know:

In general, you want to use a champion that has sustain or a strong shield, and that can outpush Nunu. For this reason I think that
could also be a very good counter to Nunu, but I am not a good Riven player; however I've seen a Riven x Nunu matchup before. Riven lost the lane hard early but after a few items she could outduel Nunu and he couldn't escape even with his Iceball due to her constant dashes.