Pete:

There is a Hampton Beach Casino in NH. Big building right on the beach. Used for concerts, meetings, etc. There were several of these types of "casinos" in the Boston area at the turn of the 19th century. I emailed the URL of your scan to an exonumia collector friend who is knowledgeable of RI stuff of the time period. If he can attribute it I'll let you know. Nice piece! Nice find!

Dave Smith in NH
"Live Free or Die"