I have 240 volts line going to sub panel which has a black, red, and ground wire (no neutral). This is the same wire that I had hooked to my 240 volt timer that I am replacing.

Problem is: I want to wire the new timer up as follows....
Wire timer 120 volts and the pump and cleaner as 240.

I did this by installing 2 double pole breakers for the pump and cleaner and a single pole 120 volt breaker for the timer.

The problem is the GFCI trips when I turn on the power to the 120 volt timer. Is that because there is no neutral wire for the line?

If I change this and wire the timer as 240 on a double pole 240 breker will that cure the problem?

Thanks

The load terminals of the GFCI must feed only their own load and touch NOTHING else. If something touches another circuit EVEN A NEUTRAL or if a NEUTRAL touches a GROUND, the GFCI will trip.

Your options:

1. Use a 220V circuit for the timer.
2. Get a GFCI with a load neutral
3. Put the GFCI's on the sub panel breakers.

Frankly, bodies of water you are going to immerse yourself and your family i s no place for amateur guesswork with regard to wiring and protection. Get professional help.