Trademarks, or lack of active ones, aside, I'm pretty sure that there's one and only one Friday the Firkinteenth — and it's in Philadelphia at the Grey Lodge Pub. Has been for over 13 years (coincidence).
J. Ryan's in Syracuse? Not so much. They opened just a little over a year ago.
I'd link to their site, but they don't have a website or Facebook page. Saw the event listed on BeerAdvocate.
Not that their competitive markets overlap (200 miles apart?), but the name is so unique I'd find it very difficult to believe they magically came up with this creative name for their upcoming event on 5/13 all by themselves.
Update: After a brief conversation with Scoats, I now see that a local (much more overlapping, fwiw) bar in Drexel Hill has named another similar event. 2312 Garrett. Scratch that, not similar, looks pretty much the same. Cask beer, Friday the 13th, need more evidence?
Poorly played, folks. Whether Friday the Firkinteenth is trademarked or not, how about we instead see some of your own creativity?