Since Providence isn't allowed to offer Happy Hour prices on drinks, sometimes they offer deals on food... the ones I know of are:
$2 bar menu until 6:30pm weekdays at McCormick's w/ puchase of $2.50 drink
$1 appetizers @ India M - W w/ purchase of $5 drink
$1 appetizers Mondays @ the Rue with purchase of an alcoholic drink
Free items off of Bistro Menu @ Zooma with purchase of alcoholic drink for ladies on Wednesdays
Can anyone add to the list?