The official answer would be NO, there is no proof in-game or in any Nintendo statements that Yoshi has a girlfriend or any such relationship. There however is some speculation that Birdo, with her feminine qualities and apparent similarity to Yoshi's species, is his girlfriend. There is unfortunately, no evidence to back this up.
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Birdo
Birdo is Yoshis girlfriend, and they are in multiple games together.
Yoshi's official name is "Yoshi".
There is not a playable purple Yoshi in Yoshi's Story,but one does appear in the game...
Yoshi does not have a wife.