I tried dying/staining Ivory about 35 years ago and was not happy with the results. The two grip panels came out different colors. Thankfully I was able to remove the Tea stain with Flitz and a rag.
After the failed above attempt, I wiped down the gun with my usual (back then) Rig #2 Gun Oil and stored the gun wrapped in S&W VCI paper. The oil reacted (over several years) with the tan-ish color of the VCI paper and turned the Ivory the exact color and tone I was looking for - could not have been happier! A total accident however the results were great! Right after that, I sent the SAA revolver off to a supposedly renowned and famous SAA Gunsmith and he said the grips "got lost" while he was working on my gun - yea, right! Needless to say, I had to have a new pair made by the original grip maker that made them for Colt in the first place - a very expensive proposition! BTW, that was the exact moment I decided I would then on become my own Gunsmith! Other than for bluing, that was the last time any of my guns left my house!
I think the "key" to the perfect aging of the grips with the Rig #2 Oil is that the Rig #2 contained a slight amount of Rig Universal Grease that was dissolved in it. That has a tan-ish color and probably helped in making the color I was looking for. This process took years and was just a series of "accidents" - not exactly a time proven method - lol.
Before trying to use tea bags or coffee, look closely at the two grip panels and note the differences. They will be more pronounced when darkened. Not saying not to try, just to note this might happen.