A yellow or gold toned off white should work, or even a very pale yellow, on the theory that Green Tea already leans to yellow-green, instead of a blue-green, like a teal. But I'm going by the images I see on my iPad, which isn't color calibrated, so as always, YMMV. Still, a decent starting point for starting a collection of paint chip samples. :)

Look at BM Carrington Beige. It's a light beige that has a slight yellow undertone. Any store should be able to color match a BM color.

If you want lighter, you could look at Behr Hazelnut Cream. I have used this in multiple rooms but in one I am seeing a green undertone which might work in this case. I love this color other than this one time. I used it in our kitchen and DH's treadmill room/man cave. Behr has some of their whites/lighter colors set up by undertone. I also like Behr's Swiss Coffee but that is even lighter.

Thanks for the suggestions! I'll be adding to my collection of paint chips tomorrow.

BM Lancaster Whitewash is a creamy off white with a greenish undertone. I painted most of my house with it and it seems to go with everything.

The wainscot actually seems to have more blue than yellow in it. Given this, what color of undertone should I aim for? Green? Yellow? Will green work with the sunny windows? I need a tutorial on undertones!

If a bluish-green probably a green undertone will work. It sounds like it is still a warmer color. Again, take a look at Hazelnut Cream (Behr). It will look neutral but certain situations will bring out the green undertone which is very subtle. You can get the little sample cans and try it out on some poster board. The little paint chip can look so different - I think the HC chip makes it look darker than it is. We have Hazelnut Cream in the kitchen (south facing) and a north facing room and it works in both which is why the green undertone I am seeing in the other room was a surprise. It stands out compared to the carpet so it isn't an ugly color that I am seeing, it just in this one room that undertone clashes with the carpet.

Edgecomb Gray might work

Can you take a pic of one of the rooms and post it here? I looked up images of Minwax Green Tea and came up with these at the link. HERE.

If you can't post a pic, do any of the pieces in the link look like the stain does in your MIL apt? I'd want to bite the bullet and paint the wainscot when you do the upper walls. I bet it would make huge difference. I forget, is your MIL going to live in the apt, or are you going to rent it?

I will try and upload some pics later today. I could be wrong about the stain color, but there was a gallon-size can of it left with the house. All the wainscot in the apartment, and all the doors in our space are stained this color.

I would prefer to paint all at once, but rents are very hard to find in the area so we feel we can wait until we replace the flooring in a year or two. (We did not even advertise, but had a potential tenant find us through word of mouth before we even closed on the place!) We are renovating the bathroom and adding a washer dryer so that might overcome the green wainscot!

What about SW Alabaster White. It is a very warm white, but not a cream. I also like the idea of SW Creamy as previously suggested by Tibbs.

In order for the color to read as green, it has to have a lot of yellow in it. Yellow + blue = green, but the blue pigment is very strong, so the formula will be predominantly yellow (and maybe some white) to "dilute" it.

A "cream" will work, but that's just yellow ocher with a little black or grey added, it's really a very neutralized yellow. A green could be tricky, because the two greens could fight, and not everyone likes that much green. Or blue.

Since this is a rental, and you have a hot market, I would just cut to the chase, paint the whole apartment BM Linen White, and call it a day.

Get that wainscoting painted NOW! Be sure to use at least one coat of BIN to seal it. Once that is done, you can start with the floors and get rid of the vinyl. Then paint the walls and go from there.

We finally landed on Glidden Crisp Linen White after a tree's worth of paint chips, and it is working really well in the space. I'm actually surprised at how nicely it is going on, although it will need 2 coats. Before pics:

Kitchen

Bedroom

Bedroom

I would love to do the wainscot now. but we just don't have time. Our tenant didn't want to wait to replace the suspended ceiling with drywall! At least the bathroom will be all new fixtures.

Thanks for all the advice, it really helped me narrow down our samples.