Subject: persistent engine miss
Question: eclipse,1992,gs,2.0 automatic,2 wheel drive,non-
turbo,135k miles difficult first start of the day-    subsequent starts o.k
persistent miss
new timing belts, tensioners,belts @ 125k
new piston rings, and valve job    "
has small exhaust manifold leak
Answer: Rich,
Cracks or small leaks in the exhaust manifold are pretty common on the 1G Eclipse, though I doubt that is causing your problem.
Check your spark plugs, plug wires, and ignition coil. If it's been 50k-60k miles since you've last changed them, now is a good time to do it.
Another common problem is your mass air flow sensor. If your intake air temperature sensor is defective, your car will hesitate on cold starts. Your pcv valve should be replaced if it over a year old. They're only about $4 and it takes less than 10 minutes to replace. Your throttle body may need to be cleaned, as well as your EGR valve. If you have more than 15,000 miles on your fuel filter, replace that too.
All of the above are relatively inexpensive, regular maintaince items that can usually be performed by yourself if you have a few tools and decent service manual. If none of that helps, you may have a faulty ECM (car's computer). The 1G DSMs (90-94 Eclipse, Talon, and Laser) had faulty computer components. The capacitors on the board would leak and ruin the board over time. People would get all sorts of strange code readings and engine problems. Typically, this only occured on the turbo models, but some bad capacitors may have found their way to the non-turbos as well. You should have it checked by a qualified technician.
Good luck!