Don't know about facilities around Corvera (although there is an airport!) but are you aware that in the Murcia area, you are required (by law) to have a licence and insurance for all fishing in rivers, lakes and embalsas. I am told the the Guardia have a squad going round checking fishing licences and insurance and, In fact, I understand that you may only fish without these documents in the sea whilst standing on land.
I don't know of any clubs in that area, but I know that there is one in the Orehuela area - look at www.abbeyangling.com and they may be able to help.
Steve