Well, I'm just confused why it doesn't work now. Alot of people around the area do not have the pressure tanks. Woudn't the pressure tank cause my pump to cycle on and off several times throughout the entire sprinkling time?
Pumps work better when they have something to push against. That's what a pressure tank provides. You will find it makes a better solution than wringing your hands over why your present setup isn't working right. If you are dead set against adding a pressure tank, then you can put back the original zone valves and tell the missus to stop complaining. Obviously, the new valves aren't giving the pump enough to push against. (zone valves with flow controls might solve the problem, but then again they might not)
A pump cycles because of a mismatch between supply and load. It is up to you to design a sprinkler system that matches the output of the pump. A pressure tank never causes cycling.