Which would make more sense? "how is thy morrow? " or "how is thine morrow? "

Neither really makes sense. However, "How wilt thine morrow be?" makes much more sense.

Edit:
(I was confused as to what you meant, for morrow means tomorrow. Morn means morning)
You could say How is your morning in many ways.
However, I personally like "Art thou well this morn?"
Seeing as there is no difference between thy and thine except for the sound, do what floats your boat with those.