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Pre-smokeless Powder
While potassium nitrate-based black powder was the de-facto standard for centuries, it was phased out for cleaner-burning, moisture-resistant and low-smoke alternatives after the end of the American Civil War. The age of a rifle can help identify it as a black powder rifle. If it was made prior to modern smokeless powders, it had to use black-powder, but not all "long guns" (non-pistol hand arms) had rifled barrels. So a long, or non-pistol, gun manufactured prior to smokeless propellant and after the advent of barrel rifling, is definitely a black powder weapon, and probably a black powder rifle.
Post-rifle
Many old long guns were not rifles; they did not employ a rifled barrel. Rifling is a corkscrew pattern in the inside diameter of the barrel that causes the bullet to spin in flight, stabilizing its trajectory and vastly improving its accuracy. While rifling technology is seen as far back as the 1500s, many early flint-lock muskets had smooth-bore barrels. Rifling showed up in muzzle-loading weapons in the mid 1800s. Notable examples include rifled muskets from the Springfield Armory and the Kentucky Rifle -- each of which became popular because of the improved accuracy of their rifled barrels.
Breech
The breech is the portion of the firearm that holds the projectile prior to firing. Breech-loading weapons allow the shooter to place the projectile from the breech, or rear, of the barrel, instead of packing powder, wad and projectile down the muzzle. Breech-loading black powder rifles have very bulky breeches. After the invention of jacketed cartridges, the cartridge itself contained much of the outward expansion of gases, taking much of the stress off the breech. Black powder guns had to withstand these expanding gases without the help of a brass cartridge sleeve. Breech-loading guns were especially vulnerable because openings and moveable parts created weak spots. Heavy breaches with flint-lock actions -- as seen on the Springfield and Kentucky Rifle -- tip you off to black powder rifles
Modern Hunting Rifles
As jacketed cartridges and smokeless powder became popular, black powder was all but abandoned. The large caliber projectiles used in black powder guns -- often .50 caliber or even larger -- gave way to smaller, high velocity rounds, often .30 caliber, .270, or smaller. Some makers matched the .50 caliber with their cartridge designs -- such as the notorious .50 Caliber Sharps Buffalo Rifles -- but jacketed .50 caliber rifles are very rare today. So, if you're looking at what appears to be a modern hunting rifle and it's a .50 caliber, you're probably looking at a contemporary black powder sporting rifle.