The ball size is normally (probably always) stamped right into the top of the coupler on the trailer... just read it and use that size. North American balls are all 1-7/8", 2", 2-5/16", or (rarely) 3", and for a trailer the size of a
Beachcomber it will almost certainly be 1-7/8" or 2". If a 2" ball fits in, that's probably the size; if it won't, it's probably 1-7/8"... but again, to be sure read the markings.
Markings are often obscured by
paint, so some
paint stripper might be called for.
It might seem like there should be a ready answer, but trailer components can change from year to year, or even day to day, so there is no way to be sure what was used on a particular brand in a particular year. Couplers are also replaced when they wear our or are damaged (or if the owner just prefers a different style), so even if we knew what it came with, we couldn't be sure what it has now.