Capt. William Hilliard Allen - Identity of William Allen, father of William Kumukoa Allen

I think it is possible that William K. Allen's father is a different William Allen (not Captain William H. Allen of CT).

Among other things, at least one census record for William K. Allen indicates that his father was born in Massachusetts, not CT.

There are a LOT of William Allens in that era, including quite a few Captain William Allens, so it's a question that requires some careful exploration and further research.

(Note: Capt. William H. Allen did pass through Hawaii in his travels, so it's not out of the question, but it would be a surprise given his relatively well-documented life - there were other William Allens in Hawaii at the time who might be more likely candidates.)