Problem with Vibration

No mil light, and I dont think its the coolant sensor, the fans come on when theyr suppose to, I think its a fuel problem, mayb that pump relay, it only takes a couple turns of the key and it starts again and runs for a bit, sometimes if I coast long enough, it will catch up w/out stalling or havin to turn key to start, and run for a bit but then itl happen over nd over til it cools down