There were no made-for-TV movies in the 1950s (the form wouldn't be introduced until the 70s), so that leaves theatrical films and TV shows shot on film. The studios at the time rarely bothered to shoot TV material on color film (since TV broadcasts were strictly black and white0, but Disney was one of the exceptions. So a TV series is a possibility.
Disney did a number of projects featuring muzzle-loading black-powder and red-coated British soldiersl, not all of them specifically "Colonial" or even American. (The Brown Bess musket and red uniform were both in use, with few changes, for the better part of a hundred years.

)
Unfortunately I don't recall many details of most of the films of the period. The
Swamp Fox TV series (shot in Technicolor) seems a possibility, although I don't know if it would have featured ships very much. The 1957 feature
Johnny Tremaine, set largely in and around Boston, certainly featured ships, but not pirates that I recall.
The Swiss Family Robinson is in the right period and all the actors were American, even if the characters weren't. It had pirates, too, but no attack on a defended town. I have a feeling you may be remembering Disney's version of
Kidnapped!, the Robert Louis Stevenson novel. (Written and directred, oddly enough, by Robert Stevenson.

) If I recall it has pirates, shipwrecks, redcoats and probably the bombardment of at least one town by a ship's guns. But it is set in Scotland.
But probably the best candidate is Disney's first-ever live action film, 1950's
Treasure Island, also based on a Stevenson novel. The tale of Jim Hawkins and Long John Silver has most of the elments you mention, if memory serves.
Hope this helps. Seems like all of these films would be fun to see again.
Regards,
Joe