I apologize in advance if this is the wrong forum for this post.

I have a 1999 4R with the 4 cylinder engine. Just in the past couple of days it has developed a bad vibration and I have no idea what it is.

It happens when I am accelerating under stress, like going up a hill for example. It seems to happen mainly above 30 mph. I can be cruising along fine but when I accelerate to increase speed or to go up a hill I start getting crazy vibrations and it almost feels as if the engine is bogging down and sputtering under stress as I accelerate. I don't think the engine is really sputtering, I think the vibrations make it seem that way. I can't tell if its the engine or what. It seems to smooth out at certain speeds, as long as I am not accelerating hard.

When the car is in park I can rev the engine as much as it can stand and it doesn't vibrate. It idles fine and seems to run smooth as silk.

Does anyone have any idea what this vibration can be?

Your description sounds like a misfire under load.
MOST times, it's a bad spark plug, on both the 5vz-fe AND the 3rz-fe.
They come with 30,000 mile plugs.
Do you know when they were last replaced, and if so, with what?
NGK and DENSO are the only way to go with plugs on these things. All the "mighty" and "autolite" and "champion", "bosch" and the like seem to be a worse alternative than leaving old worn out NGK or Denso plugs in them.
After plugs, plug wires are usually the next culprit, with some having an injector problem, some of the 3 and 3 rz's had valves get too tight and creat misfires at IDLE, not under load accelerating.

So.... start with looking at the plugs.