you want to paint the frame why? looks fine in black. (if you mean paint the unit, no. you need contrast. If you paint it white it's just going to disappear)

examples

You could do something like this

YOu can get something like this at World Market

You mean the credenza? Paint it the same as the wall if you want it to blend in. Only use a different finish. A satin or gloss.

I see now you said you want a white. BM Chantilly Lace then.

I do like the 4th picture. I wouldn’t be painting the whole unit white, I would still leave the top the same wood tone, similar to picture 4

why not a soft gray such as BM Classic Gray

The chest is so dark now that it loses all detail (at least in the photo). Painting it a lighter color should bring out some of the detail which would just enhance the piece.

You already have 4 0r 5 whites on that cabinet , the wall, the runner the lamp, the bowl and the matting why add another to drive you crazy The contrast is nice it makes the art stand out.

I think the art will still stand out as the top of the cabinet is will remain the same.

BM Cloud Cover

I think match the wall or go with a nice contrasting colour to let it stand out

OOPS reread No paint on the cabinet , too many whites already though

Painting the sides white will feel patchy and busy. Rethinking accessorizes will transform it and look to complement the art a bit better. Maybe start with removing the runner and test until you feel everything connects visually.