2000 Hyundai Sonata ran through emissions twice/ vibration

We just bought a 2000 hyundai sonata and we have ran it through emissions twice and both times they said it has to go through a drive cycle. We have drove it about 1000 miles and the check engine light does not come on. We had it tested and it works though. Could the drive train sensor be bad? Also when you drive it there is a vibration at about 40-45 mph and after. It gets worse when you give it gas to pick up speed and lets up when you let off the gas. Tjought it could be a miss so I replaced the spark plugs and wires along with a busted coil. It helped a little but it still does it. Don, t know what to check out now to see if it could be the problem. Could you please give me some ideas as to what could be the problem? Mike