Hi Jo
I might be too late, but there is 'The Amathus Riding Club' run by Costas and his British, BHS trained wife Denyse, in Pareklishia limassol, I have just started riding there, and there is also a chap called Vatchic' at the Elias Country Club, Paraklesia, just opposite.
Both are about 10 mins from the Armenohuri exit of the highway, Limassol.
I would recommend Costas' place as I have recently ridden there. Denyse number (00357) 99604109 & Costas (00357) 99348045
The number for the Elias country club or 'Santa Marina Retreat is (00357) 99545454 ask for Nadia or Vatchic.
I have not ridden there yet, just looked around.
I am not sure if either can get access to the beaches in Limassol. But riding in the mountains is beautful.