I was brought up in W London, and always took this to be 'roll or bowl a ball'. When I was a girl (early fifties), the coconuts were on quite small stands and you could either roll the hard wooden bowl along the (bumpy grass) pitch or throw it underarm, attempting to knock a coconut off its stand.
This was notoriously difficult and we always suspected foul play (as in a bit of glue)
The fairgrounds had nothing to do with sailors or shanty stuff. And the whole song is typical Cockney banter. Billy Cotton used to sing it (it's on Youtube) The innuendo of "I've got a luvverly bunch of coconuts!" would make everyone giggle. Rather like the Marrow Song (same era) "Oh, what a beauty! I've never seen one as big as that before!" We were rather a smutty-minded lot in those days!