Does it mean something like "I wouldn't have given you (meyil) if I didn't have a heart"? What does "meyil" mean here? I checked zargan for the meaning, and none of the meanings there seem to fit here.
'gönlü olmak' is an idiom, a synonym of 'istemek'. And 'meyil vermek' is like 'sevmek'. So in English, it should be something like ''I wouldn't love you if I didn't want (you)''.
Hazal you are right, but with "gönlüm olmayaydı" one could also intend to say "if I didn't have a heart". And I think the latter one is more appropriate here. (I wouldn't fall in love with/love you, if I didn't have a heart." )