"My dad drinks wine."
Translation:Mio papà beve vino.
You should be able to, because with papà, mamma, babbo, nonno, and nonna the use of the article is optional according to this site http://www.uvm.edu/~cmazzoni/3grammatica/grammatica/possessives.html
EDIT: It may say it's optional but duoligno may or may not agree, in those cases just use the report button.
I've been reporting and reporting the same stuff for a while now and it doesn't seem to change. Also, the way duo presented this sentence to me was one of the ones with three options where you have to choose the correct one. The english sentence was using "dad" and every option had "padre" instead of "papà" and yet I was JUST marked incorrect for translating dad as padre before and lost a heart for it. Such phooey.