The first US gun laws pertaining to citizens were passed in the 1930s, prior to that the only laws I'm aware of related to slaves and former slaves having weapons, more specifically how they were not allowed to. I don't think puckle guns were a common enough item for people to be worried about them since I don't believe any ever came to the US.

A number of private citizens owned cannons. Merchantmen in particular might have a few on their ships. We know that John Stutter got one from the Russians when he purchased Fort Ross in 1841. Up to 1856 the US was quite happy to employ privateers, meaning that there were privately owned warships in the US, which would imply that the owners had cannons on board. During the Civil War you got blockade runners and various volunteer "most certainly not privateers at all, no siree." So at least until the Civil War, and most likely for a decade or so past that, you'd have US citizens privately owning some of the most powerful weapons of their day.

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