In October and November? Any day you want.

Airlines try to make award seats available when they don't otherwise expect to sell seats. And when award seats are available, there are some times that there's just going to be more competition for them.

I'd say the hardest days to get an award seat to the Carribean during high season would be Thursday and Friday (especially), and the hardest days to get award seats back from the Carribean during high season would be Sunday (especially) and Monday.

Why?

First, people are going to buy those seats. Flights are likely to be full, so the airlines don't want to give them away.

Second, lots of frequent flyers are going to be competing to redeem the seats that are going to be given away on those days.

Shoot for Wednesday.

Seriously, though, I've redeemed awards to the Carribean in February heading down on Thursday, back on Sunday. Don't think it's impossible or even necessarily difficult.