Dyeing Dye tan skinned to black, any tips?

Black is thankfully the easiest color to dye, since you don't need to worry about uneven parts, streaks or accidentally dyeing it too dark. You just keep dipping until it's nice and saturated.
Painting would definitely not be the better choice, since it would be streaky, thick and chip off right away anyway.

You can use both iDye Poly and Rit Dyemore, they both work just fine. It's a bit of a personal preference. I always used Rit Dyemore since it was easier to get and always had the colors I needed. For black, they only have Graphite, but it's still very dark. You can add a tiny bit of dark blue for a colder black, if your doll has a light tan before.

 

I've only dyed vinyl toys, so my advice may not be particularly applicable here, but... From what I've seen, you can use either, as long as it's the normal RIT and not the one intended for synthetics (as it seems to give very inconsistent results? this of course could be user error lol).
EDIT: of course while I'm typing someone says it works for them. Maybe look at what colors each has available and decide which will give you the black you want!

I would say RIT might be a hair more convenient, because iDye Poly is a powder and thus requires measurements, thorough mixing, etc. It's given me some great results though! Again, grain of salt for that since I used it on vinyl, but it's widely used by disc golf players as well.

These videos by Lomi really helped me with understanding the dye procedure and what to expect:
My first time dyeing a BJD
Removing dye from a BJD / using iDye Poly
An easy fix for uneven dye results
Dyeing a BJD with jointed hands

 

No, one should use specifically the one for synthetics. Resin is closer to being, well, plastic than a natural fiber like wool

 

Here's a brief guide by the master of dyeing dolls black- Mismantis. In short, she used iDye Poly, dyes the pieces for longer than necessary, and scrubs the hell out of them afterwards to get off excess dye. The doll in this example is even a tan one!

 

Keep in mind that if you dye a doll whatever faceup you do will be permanent as there’s no way to remove MSC from a dyed doll without either removing the dye or affecting the resin itself. Painting can work if you work in layers, use a soft brush, and have a way to thin out the acrylics (Liquitex flow medium is great for this but water also works) but as others have said, it’s likely to chip so I’d dye the body and paint the head only. There’s also no way to remove faceups on acrylic paint but it’s much easier to just paint something vs. doing the whole dye setup.

 

There are several different dyes that one can use on Resin, it depends on exactly what you are going for. Here is a comparison in the Workshop about different dyes and how they managed/took to the resin. I've never personally dyed a doll (yet) but I have seen better results (in person and online) with iDye Poly or the Synthetic Rit Dyemore