You might want to contact the Hotel Herradura Golf Resort
http://www.hotelherradura.com/golf/index.htm. They are located about halfway between the airport and downtown. Their website says they offer lessons but does not include further details. Their green fees run about $40/pp, cart rental is another $25 and if you don't want to haul down your clubs that is another $20.
Here is one free golf lesson CRT-style that I picked up from other members. If you need "cover" for your activities in CR, bring extra golf shirts with you on the day you go golfing and have photos taken with you in the different shirts that you can show others when you go back to prove you did nothing but go golfing everyday. It really cracks me up the ingenious lengths that the married guys go through to cover their tracks.