Without seeing the colors in your rug, selecting the lightest color and matching paint to it might look nice - unless the lightest color is gray, since you have tried that and it looks cold. Also, does the dining room adjoin the living or family room? If so, you may want to paint both rooms the same color, or one of the rooms slighty darker than the other for a cohesive look.

Gray is a cool color. You may want to use a warm color in this room. What are the other colors in the room? Please do show us a picture of the rug.

Warm colors: off-white, cream, tan, brown, olive green, rust, orange, peach, golden yellow, orange-red.

Cool colors: bright white, gray, taupe, navy, black, royal blue, emerald green, purple, violet, fuchsia, ice pastels, forest green, lime green, blue-red.

Here is Sherwin-Williams' read on your rug:

I think a gray and green combo would be beautiful.