All Pokemon's max happiness is 255; and the amount of happiness can be judged by calling Bianca on the Xtransceiver, who will evaluate your Pokemon happiness. A lady in the Icirrus City Fan Club will do the same.
If you have max happiness, Bianca will say:
"What great friends you are! It's so nice how you trust each other! It makes me kinda jealous!"
If you have max happiness, the lady in Icirrus City will say:
"It's super friendly to you! I'm a bit jealous!"