No. Potions do not increase friendship. Here are items that can increase friendship:
Friendship increasing Berries
Grepa, Hondew, Kelpsy, Pomeg, Qualot, and Tamato all increase Friendship, although you lose some EVs in turn.
Soothe Bell
If a Pokémon is holding a Soothe Bell, increases to its friendship are boosted by 50% of the change. Basically, you increase the amount of Friendship you get when you hold this Item. Source
Alternatively, other ways you can obtain Friendship is by leveling them up, giving them Vitamins, (e.g Protein, Carbos, Zinc) catching the Pokemon in Luxury / Friend Balls, etc.