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The short answer is yes.
The long answer..... According to the ATF, a black power rifle is not considered a banned firearm as it is a replica of an antique firearm and is considered the same as an antique, even if brand new. Felons are not prohibited from owning antique firearms.
From the ATF site:
1. Can a person prohibited by law from possessing a firearm acquire and use a black powder muzzle loading firearm?
The Gun Control Act of 1968 (GCA) prohibits felons and certain other persons from possessing or receiving firearms and ammunition (“prohibited persons”). These categories can be found at 18 U.S.C. § 922(g) and (n) in http://atf.gov/publications/download/p/atf-p-5300-4.pdf.
However, Federal law does not prohibit these persons from possessing or receiving an antique firearm. The term “antique firearm” means any firearm (including any firearm with a matchlock, flintlock, percussion cap, or similar type of ignition system) manufactured in or before 1898. The definition includes any replica of an antique firearm if it is not designed or redesigned for using rimfire or conventional centerfire fixed ammunition, or uses rimfire or conventional centerfire ammunition which is no longer manufactured in the United States, and which is not readily available in ordinary channels of commercial trade. Further, any muzzle loading rifle, shotgun, or pistol which is designed to use black powder or black powder substitute, and which cannot use fixed ammunition, is an “antique firearm” unless it (1) incorporates a firearm frame or receiver; (2) is a firearm which is converted into a muzzle loading weapon; or (3) is a muzzle loading weapon which can be readily converted to fire fixed ammunition by replacing the barrel, bolt, breechblock, or any combination thereof. See 18 U.S.C. § 921(a)(3), (a)(16).
Thus, a muzzle loading weapon that meets the definition of an “antique firearm” is not a firearm and may lawfully be received and possessed by a prohibited person under the GCA.
In addition, the GCA defines the term “ammunition” to mean “ammunition or cartridge cases, primers, bullets, or propellant powder designed for use in any firearm.” Because an “antique firearm” is not a “firearm,” it would is lawful for a prohibited person to receive or possess black powder designed for use in an “antique firearm.” Also, the Federal explosives laws do not make it unlawful for a prohibited person to acquire and possess black powder in quantities not exceeding fifty pounds if it is intended to be used solely for sporting, recreational, or cultural purposes in “antique firearms.” See 18 U.S.C. § 845(a)(5)
By contrast, a prohibited person may not receive or possess black powder firearms that can be readily converted to fire fixed ammunition by replacing the barrel, bolt, breechblock, or any combination thereof. ATF has classified certain muzzle loading models as firearms. All of these models incorporate the frame or receiver of a firearm that is capable of accepting barrels designed to fire conventional rimfire or centerfire fixed ammunition. These muzzle loading models do not meet the definition of “antique firearm” as that term is defined in 18 U.S.C. § 921(a)(16), and are “firearms” as defined in 18 U.S.C. § 921(a)(3). Furthermore, as firearms, these and similar models, regardless of the barrel installed on the firearm or provided with the firearm, are subject to all provisions of the GCA. Persons who purchase these firearms from licensed dealers are required to fill out a Firearms Transaction Record, ATF Form 4473, and are subject to a National Instant Criminal Background Check System (NICS) check. Felons and other prohibited persons may not lawfully receive or possess these firearms or ammunition.
The following is a list of weapons that load from the muzzle and are classified as firearms, not antiques, under the GCA, because they incorporate the frame or receiver of a firearm:
• Savage Model 10ML (early, 1st version)
• Mossberg 500 shotgun with muzzle loading barrel
• Remington 870 shotgun with muzzle loading barrel
• Mauser 98 rifle with muzzle loading barrel
• SKS rifle with muzzle loading barrel
• PB sM10 pistol with muzzle loading barrel
• H&R/New England Firearm Huntsman
• Thompson Center Encore/Contender
• Rossi .50 muzzle loading rifle
So yes, you can own a black powder revolver or musket as long as it is not on the excluded list...