Frontier Airlines has the best oversized baggage policy to CR from the US in the industry right now. Their kayak policy looks OK, but they only take them on an AirBus (supposedly that is what they usually fly to CR).
Baggage Chart - Frontier Airlines
It is only $75 for an oversized item:
Checked Baggage - Frontier Airlines
For a surfboard I paid $75 each way this summer which is much less than anyone else but the size restriction was pretty limiting. Their kayak policy actually looks better than their surfboard policy because the size limit is MUCH bigger for boats. If I ever want to take a longboard down there I'll just tell them it is a kayak.
The best thing about Frontier is that they fly direct to SJO from DEN... but they don't do it in the off season. I think Dec. 16 is when they start flying again.