2006 HH vibration when starting engine and check engine light on

For the past month, my check engine light has been coming on and is accompanied by a sputtering vibration of the engine when I start the car. The vibration only happens about one out of every ten starts. It lasts for 5 to 10 seconds and then stops. I’ve taken it to Toyota twice. The first time they got a “misfire” code from the scanner, so they changed a fuel injector. When I brought it back 3 weeks later when the vibration had never stopped and the engine light was back on, they got a “coil” code for the same injector they had just fixed. A week has passed, it still vibrates (is getting worse!) and the check engine light is back on. Please help! My HH has 190,000 miles on it and I’d love to keep it going.

Any time an engine has a performance problem the first step should always be a compression test to verify there are no mechanical faults in the engine proper.
Unfortunately, seldom is this ever done.

This can lead to throwing parts at a problem until infinity with no improvement whatsoever; a.k.a. throwing mud at the wall and seeing if any of it sticks.

A cylinder, or the plural of that word, that is down can cause vibration problems, poor performance, CEL on, misfire codes, etc.
You always, and I mean ALWAYS in caps, weed out an engine problem first thing, and especially so on a 190k miles engine.

Try to always get the actual code, not the description when you have a CEL (Check Engine Light) The code will be something like [P1234] The descriptions "“coil” code for the same injector " or ““misfire” code” does not tell the whole story. The usual error is to use those descriptions as if they were diagnosis which they are not.

The codes are just the fist step and point to an area which then needs to be diagnosed by you or a mechanic, rather than throwing parts at it.