i need help with my 90 miata please!

I have a 1990 miata and i truly love my car. I just had the whole timing redone in it. the woodruff key broke off and i had to get it fixed. It ran fine even great for about 2 months afterwards. Now i am having some trouble with it i cant figure out. When I crank the car the first time of the day it acts like it is not getting any gas to the engine. i can push the pedal and it sputters and misses and then after about a minute it starts to pick up a little then it revs on up but i have to keep reving the engine for awhile before the idle will stay to a point to where the car won't die. After it heats up it runs fine. Usually about 4 miles down the road. When i stop the car and start it again it sometimes runs normal with a good idle and sometimes it does this again. I have had new plugs, wires, fuel pump and cleaned the injectors. I have also had my alternator tested and i am still confused as to what is causing my car to run fine half the time and really bad the other half. Lately it seems that while i am driving it the motor is being lugged down also. if anyone has heard of this or has a suggestion on what it may be i would be grateful to hear it! thanks wendy