You have no Constitutional right to drive a car. You have no Constitutional right to a lot of things. But we do have a Second Amendment and it permits the right to bear arms. Limiting guns to people under 21 is not unreasonable and would almost certainly pass muster if a Federal law were enacted to that effect. Limiting access if the person is a convicted felon would probably also pass muster if narrowly construed and containing protections that would permit removing the restriction in some circumstances. You're never going to get guns out of the hands of criminals, though. They get illegal guns now already anyway.
You have to keep the restrictions carefully tailored to avoid too much discretion on the part of the government. Not letting "depressed people" get guns, for example, would be a non-starter.
ἡ δὲ κἀκ τριῶν τρυπημάτων ἐργαζομένη ἐνεκάλει τῇ φύσει, δυσφορουμένη, ὅτι δὴ μὴ καὶ τοὺς τιτθοὺς αὐτῇ εὐρύτερον ἢ νῦν εἰσι τρυπώη, ὅπως καὶ ἄλλην ἐνταῦθα μίξιν ἐπιτεχνᾶσθαι δυνατὴ εἴη. – Procopius
Ummaka qinnassa nīk!
*MySmiley*
