In the 9+ years I've been on Nevis don't recall ever seeing anyone surfing.
If you did surf, the best place would be Windward Beach (on the Atlantic side near the Horse Race Track). That's the place with the best wave action but currents and undertows there can be quite strong.
Sorry, don't know of anyone who rents boards but you could try contacting Oualie Beach (www.oualiebeach.com
or 869-469-9735). They have widsurfers for rent so if anyone has regular surfboards it will be them.