The book the "Breach Loading Single Shot Match Rifle" by Ned Roberts and Ken Waters has descriptions & pictures of various early Stevens rifles.
A brief excerpt from page 38-9 that may help you ID your rifle is:
". . . the earliest models were light rifles chambered for the 22, 32, 38, and 44 rimfire
cartridges, but by 1875 centerfire rifles were available and a serious effort was being made to
interest the growing numbers of match shooters. New special Stevens reloadable cartridges were
introduced, including the 38—35, 38—45, 44—50, and 44—65, all having the then new straight
case with Boxer-type primer. In addition, the popular 38 and 44 Extra Long centerfires were
offered. Between 1872 and 1888, a total of sixteen models, sporting and target, all of tip-up type, were placed on the market and known variously as “Open Sight Rifles” (Nos. 1 and 2), “Combined Sight Rifles” (Nos. 3 and 4), “Expert” (Nos. 5 and 6), “Premier” (Nos. 7 and 8), “New Model Range” (Nos. 9 and 10), “Ladies” (Nos. 11, 12, 13, and 14), and “Crack Shot Rifles” (Nos. 15 and 16).
These frames were of cast steel, nickel plated, and perfectly safe with the black powder
cartridges for which they were intended, but it was necessary to place the hammer at half-cock
before attempting to open the action and reload, to prevent both breaking the projecting firing pin and accidental firing of the new cartridge when the breech was snapped closed."
A picture on p. 40 shows a rifle with a hinged breach like a break open shotgun and with considerable belly in the rounded receiver, a nearly round trigger guard and a ornate finger guard. The book is a good source and has some additional info that may help you.