There are two places where you can check your Pokemon's happiness, Nacrene City and the Icirrus FanClub. The rate in Icirrus City will give you a better rating of your Pokemon's happiness in terms of being specific.
Nacrene City
"It's very friendly toward you! It must be happy with you." 120-255
"It's a little bit friendly to you… Something like that." 70-119
"Hmmm… It may still take some time." 0-69
Icirrus City
"It is super friendly to you! I'm a bit jealous!" 255
"It is quite friendly to you! You must be a kind person!" 195-254
"It is friendly to you. It must be happy with you." 150-194
"It is a little friendly to you… That's what I'm getting." 100-149
"The relationship is neither good nor bad… It looks neutral." 70-99
"Hmmm… It may not like you very much." 1-69
"By any chance, you… Are you a very strict person? I feel that it really doesn't like you…" 0
