There is no Jewish Deli in the Providence metro. You'll have to go to Brookline, MA to find that.
There also isn't even a New York style deli in the metro either now that Barney's closed (and calling it New York style would be a stretch). Sharon, MA may have one, but I'm not 100% sure... Mohegan Sun may have one as well...
Sorry... I think it's a big hole in Providence's dining offerings.