Paint

To find a wall color to pair with brown wood tones, look at the wood's undertone, then use the hues across from it on the color wheel. 

Suggested palettes -

Toast + Swedish Blue + Pale Sage: coat the walls with the brown, then mix in equal amounts of blue and green accents.

Taupe + Prussian Blue + Red: Offset this bold palette with light gray fabrics and lots of metallic touches.

Yellow visually expands a room, great to use in transition spaces - hallways, and entryways. Layer yellows with deep plum, fresh green, and periwinkle.

Unless you're a diehard coral fan, this hue is more versatile as an accent than a wall color.  Because coral can be bold, and vibrant it requires the contrast of somthing cool and calming.  Peacock blue, sage green, khaki, and putty are all good partners.  White is a natural with coral for wall trim, furniture, and accessories.

Tone it down with brown-ness. Use orange in a contained room so the strong color doesn't overwhelm adjoining spaces. Stretch it, do the baseboards in the wall color, it is very elongating but keep a white ceiling. Hot pink, pale pink, olive green, and robin's egg are all good color pairings. But NEVER black.

Suggested palettes -
cress + deep orange + plum
pumpkin + blush + blue.