My '99 Tacoma V6 started vibrating whenever I would give it gas. Then it felt like it was not sending fuel out of the injectors even though I had the pedal down. When that started it threw a code for a bad TPS. So I replaced that and it is giving the engine gas, however it still vibrates when I accelerate. Are these related or is something else causing the vibration? It is not showing any code after I replaced the TPS. Again, it only vibrates when I am giving it gas, as soon as I let off it is smooth.
It is a Maunal Tranny. I just had the Tires rotated and Balanced about 600 miles ago. It definitly feels like the vibe is coming from the engine area. Could dirty fuel injectors cause it?

Given that you believe the vibration to be from the engine, the 5VZ has 3 coils on the right bank which fire those plugs directly and then wires that run to the left bank. I have seen a lot of higher mileage coils fail, so that is a possibility. If the coil is going out, it can cause what you are describing, either missing on the one cylinder or both that that coil is firing. Also, those engines are designed to run on dual electrode plugs, and do not perform well on single, or for that matter, any plugs that are not Nippondenso (Toyota) or NGK. I would go for pulling the plugs out and checking them first, followed by checking the wires and coils next. Injectors can cause what you are describing, but generally will show up at an idle.

Assuming the problem is ignition, the reason it does what you are describing is that there is not enough fire to ignite the fuel mixture under the increased load. But after you back off and the pressures drop, the cylinder goes back to firing. That's why I think it may be in the ignition.

Good luck!

You can either have a shop, or you yourself check your motor and tranny mounts. If they are broken or bad, it will cause excess vibration.

Them damn Toyotas.
Your vibration really needs to be felt before anyone can give good advice.

Not really sure what kind of "vibration" you are talking about.
In motor? In tranny? In tires? Just not enough input.... must terminate answer.

Could bad ignition, it could even be a broken motor mount.
Should be a cheap easy fix, have a shop take a glance at it.

Did you check the tires, proper inflation, tires balanced, allignment...after that I would check the transmission.