Hard to suggest colors w/o seeing the room, floors, rug, etc. Ceiling height?

However, since your LR has a south-facing window and you want to do the two rooms in the same color, I'd do the DR in the same color only deepened by 50% or so.

The floors will be re-done, in a carpet of some sort probably. The ceilings are 9 foot. Right now the trim is a painted white.

Ditto Tibbrix. Photos are needed, and a deeper shade of the LR color would be nice.

The OP is planning to repaint the LR at the same time. What furniture will you have in the LR?
I suggest two shades similar to BM Mount Saint Anne for the two rooms. I see several that would work on the EK website but I couldn't figure out the names. I think they would blend nicely with your Ashen Green and help create a lighter, modern feel.

BM Mount Saint Anne is a gorgeous color and would be beautiful with mahogany furniture. So, if you used Mt. St. Anne in the DR, use, say, BM Nelson Blue in the LR, which is a very ethereal lighter version of both Mt. St. Anne and Quiet Moments, and is like the sea, but would be great in a room with southern light flowing into it. The segue from Nelson Blue to Mt. St. Anne would be perfect as well.

Well, I have a friend who has very traditional mahogany furniture but very bright, contemporary paint colors, e.g. for her dining room something like this:

Or get some unusual art work and less traditional light fixture, e.g.

In line with nosoccermom's post, friends of mine own an old Victorian. They have more or less traditional mahogany dining room furniture, but modern sensibilities. They painted the walls turquoise. The room really looks very nice.

This is Italian Rose

I think mahogany looks great with any color. And mixing traditional furniture with new stuff makes the room look natural.

I always vote for the darker the better. Maybe a deep green or turquoise. But that rich dining set and the grey walls above looked fantastic! Or maybe a plum. What color do you want? Especially with white trim, any color is doable.

Cant wait to see pictures with what you decided!

If you like a more monochrome look, I used BM greenfield pumpkin in my last home. Looked very bronzy. I had wainscoting that was a creamy tan below. Dark cherry table and chairs, mahogany side board, and dark hardwoods.

I don't have the sample board, but the EK Sky is from the same family as the Ash Green -- although she describes it as a restful and a bedroom color, that combo of greyed green and blue work quite well in the last picture @nosoc posted. You could pair it with a more transitional chandy and some new seat fabric to "loosen up" the look. (I had a similar issue -- which I'm still trying to finish solving)

Thank you all for the thoughts. I really like the idea of the gray, and the blues. Neither of which I had on my radar. It just helps me think outside the box, so when I finally decide on something it will really be what I like since I went through all the options.

Gray is especially appealing to me. I do not have it anywhere else. I am wondering if it looks good though because of how it is everywhere right now?

I've had gray and blue for 20+ years (and yellow).
You could also go with a darker charcoal in the DR (like that art work) and the same but lighter gray for the LR.

Do go darker in the DR and get great lighting. It'll be a wonderful place to dine.

I do like the idea of a dark charcoal. Great point of going different shades due to lighting.
If anyone has any cool light fixtures or chair fabrics to get me started please share!