Like an engine vibration felt inside the car?
Make sure that the exhaust or something on the back of the engine isn't contacting the firewall/floor when in gear. The engine/transaxle tips back when put in a forward gear,
The motor mounts are adjustable in slotted brackets if a metal-to-metal contact is occurring. The engine/transaxle can be moved right/left or tilted forwards/backwards slightly. Don't move more than a 1/4" or the axle joints may bottom out.
Use a pry-bar to move the engine/transaxle around while someone is inside the car in drive and listening for changes in the noise.
Will giving the car gas, or putting it in neutral make any difference? It could be that the engine is struggling to stay running (for a variety of reasons, choked for air/starved for fuel, vacuum issues, etc, etc) with a load on it.