If the director wants a Fiddler number, Miracle of Miracles
would be the obvious choice. If he wants non-Fiddler, a good bet might be Standing On The Corner (Watching All The Girls Go By)
from The Most Happy Fella.
Equally important, if not more so, than singing is showing Motel's development as a person, from a shy nobody petrified at first of Tevye to a respected citizen in his own right. Leonard Frey in the movie is a good counter-example: he had a nervous laugh that he never shook free of, long after the character should have. IMO he was an unmitigated disaster, so bad that John Cleese couldn't have done worse! I can almost hear Cleese screeching Motel's make-or-break line "Even a poor tailor is entitled to some happiness!", maybe interjecting a "bloody", in the same tone I would expect to hear "This is an ex-parrot!" (an apt metaphor, BTW, for arranged marriages).