To get points through a credit card you would need to apply, get the card, hit the minimum spend on the card, and then wait for that statement to close to get the bonus. The only exception that I know of is the Alaska Airlines Visa which gives 25,000 points upon approval, however, they wouldn't be an option to the Caribbean. With wanting to travel so soon, your best (maybe only) option is to pay cash for a ticket. If you just want to get somewhere cheap and have some flexibility in your travel dates you should consider Frontier, Spirit, or Allegiant, as they often have sales as low as $20 each way (make sure to be aware of all additional fees before booking).