We use SkyKing frequently to travel between POP and Providenciales, Turks and Caicos. They use CaribAir planes for doing charters. You can call them in Providenciales at 649-9419464. They'll put on a charter flight for you.
Alternatively, speak to Glenn de la Rosa, who is their manager at POP. He is usually at the POP SkyKing check in desk from about 10 am to about 2pm on Mondays, Wednesday, Fridays and Saturdays.
If you need further information, send me a pm or e-mail. We know the outfit quite well.