I did some flying while in Antigua last February.
It's not strictly self fly hire in the sense that the aircraft owner comes with the aircraft but you sit in the left seat, do all the flying and take passengers in the back if you wish. It didn't bother me because I always fly with a local when flying in a new country for the first time.
Aircraft: PA28-161, Registration V2-LDW.
Contact: David Hart on +1 268 463 3000.
He's a civil engineer, and used to instruct in California before moving to Antigua some years ago.
I flew around Antigua and also over Montserrat and on to Nevis and St Kitts.
English Harbour
Horseshoe Bay
Montserrat is worth seeing but, unless the new airport is completed by the time you go, you won't be able to land. The original airport was destroyed by the volcano a few years ago and is unlikely to reopen for a very long time, if ever.
Nevis is a small friendly airfield and they'll let you fly around the island, do a touch and go or land, as you wish.
St Kitts airport is bigger and busier. I flew around part of the island but was then given (firmly non-negotiable) options of landing or going away immediately! I didn't have time to land so headed back to Antigua - No 2 to land behind the inbound Virgin 747-400 which flew us home a couple of hours later.
I didn't go to Barbuda but I'm told it's a pretty island - Antigua has wonderful deserted beaches (if you get away from the hotels), but pretty it is not.
David's happy to do longer flights to other islands if required, and is very pleasant company