Sure, it's possible; the question, really, is why. Vikings would be far out of their element in the Caribbean, and they weren't short on space in their accustomed environment, so it would take a lot of pressure to send them there. Besides, at those distances a Norse colony would be more or less completely cut off from the rest of the Viking civilization, so would have to supply itself. I'd suggest religious persecution as a motivation, but you asked for a Catholic kingdom at a time when Catholicism would have been fine, and in any case they wouldn't need to go so far.
So let's tweak history a little. There's evidence that a volcanic winter occurred about seventy thousand years ago, due to the eruption of a supervolcano. How about we do it again, and use a different one - there's a supervolcano in Italy, called Campi Flegrei. It's a little on the small side, so let's imagine that in this alternate history it was a bit bigger, and erupted in the early 1000's. The resulting cloud of ash would have caused several years of cold temperatures worldwide, especially in Europe, North America, and - most importantly, for our purposes - Scandinavia. Crops would have failed, game animals would have reduced populations. It wouldn't be enough to kill anyone off, but perhaps enough that a few daring seafarers might envision a better place, a region far enough southwest that the effects of the ash cloud would be reduced. They set out from Iceland and keep going south until things warm up, then make landfall, founding a Viking colony in the Caribbean. Four hundred years later, this colony has become a kingdom in its own right.
Mind you, I'm no meteorologist, nor am I a vulcanologist - any or all of this could be nonsense. But it seems plausible to me.