No he cannot get in trouble because he is a felon.
The only Massachusetts General Laws pertaining to BB guns, that I am aware of, are MGL Chapter 269 Sections 12A and 12B. 12A pertains to sales of BB guns and 12B is below for your reference.
CRIMES AGAINST PUBLIC PEACE
Section 12B Air rifles; possession by minors; shooting
.Section 12B. No minor under the age of eighteen shall have an air rifle or so-called BB gun in his possession while in any place to which the public has a right of access unless he is accompanied by an adult or unless he is the holder of a sporting or hunting license and has on his person a permit from the chief of police of the town in which he resides granting him the right of such possession. No person shall discharge a BB shot, pellet or other object from an air rifle or so-called BB gun into, from or across any street, alley, public way or railroad or railway right of way, and no minor under the age of eighteen shall discharge a BB shot, pellet or other object from an air rifle or BB gun unless he is accompanied by an adult or is the holder of a sporting or hunting license. Whoever violates this section shall be punished by a fine of not more than one hundred dollars, and the air rifle or BB gun or other weapon shall be confiscated. Upon a conviction of a violation of this section the air rifle or BB gun or other weapon shall, by the written authority of the court, be forwarded to the colonel of the state police, who may dispose of said article in the same manner as prescribed in section ten.