I was thinking Straits Settlements or Newfoundland, and perhaps a 50c piece with that diameter, but couldn't match it up. The reverse has a crest in the middle with scrolls under, sort of like South African issues (but no matches there either).
here's an example of the Jamaica Penny (30mm): http://museumvictoria.com.au/collections/items/82248/coin-1-penny-jamaica-1869?image=520532
Yup, looks like Jamaica. Was the penny the largest denomination that circulated in Jamaica in the 19th century? How on earth did that work?
Yes, they didn't use larger denominations in Caribbean colonies such as Jamaica, Barbados, Bermuda like they did with colonies in Latin America and Asia.
So, how did they carry out commerce? Wagonloads of pennies? Or did they use silver coinage from the rest of the empire to fill the gap?
I would venture a guess that the locals (i.e. slaves) would not have needed larger denominations for purchasing goods. The British colonialists must have carried out transactions with British homeland currency.