89 Civic idle problem

Hi there. I'm new to the forums. Anyway, I have a 1989 Civic DX sedan. The car runs fine but sputters a lot when idle. When it gets hot (thats about 98% of the time in Puerto Rico) the idle goes down or up. The Check Engine light never goes on but seems to be working. Also the ECU doesn't display any code. What could be causing this??? Also I noticed that whenever I hold the throtle down for a long period of time while the car is in park a little bit of water come out the moufler. What can cause this??? Any help from you guys is gratly appreciated.

Try to do a tune up? Usually when it sputters like that i would tune it.

I changed the oil and air filter, as well as the oil. I also put a new timing belt and the car still has the idle problem. I don't know what else to do.