I'm not a small-arms expert by any means, but perhaps some words from Flayderman's GUIDE TO ANTIQUE AMERICAN FIREARMS 2007 edition will be useful, even though Tryon muskets, not rifles, are discussed:
pp. 554 under "Tryon Republic of Texas Musket" ...total quantity 1500...(long discussion of disposition of those not paid for by Texas and returned) Surviving specimens are very rare...Tryon not known to have any other state or U.S. contracts for flintlock muskets. Be cautious of spurious markings."
I'm thinking Flayderman would have mentioned something about Tryon rifles if he knew Tryon had received a state contract, even though he's only discussing muskets here.
There's nothing I could find in this Flayderman edition regarding a Tryon military percussion rifle.
I'd think after as many editions as Fladerman has had, if the Tryon rifle you mention could be called a "Secondary military longarm" it would show up in chapter IX-B even if only a few examples were known.
Again, I don't know much about small arms, just wanted to give you wnat's in (NOT in actually) the latest "Flayderman."
To Join the Company of Military Historians click here