I've had a few different vibration issues that only occurred during light acceleration and they weren't the coils or plugs. One problem was the cv joint axles being worn out and very wobbly. The other problem was the torque converter clutch being worn out.
To check each axle you have to put in neutral with the brake set. Then grab each axle and try to rotate and move around. They shouldn't really move much. Mine were able to clunk and flop all over the place.