There are a couple of ways...
The easiest is to put a "color filter" layer over the whole screen (like Cassiebsg says): this will tint the background, characters and objects all together. Just create a full-screen (non-clickable) GUI, set its background to the color you want, and set its transparency to the right level.
The other is to copy the background onto a DynamicSprite, tint that, and then draw it back to the background:
DynamicSprite* bgSprite = DynamicSprite.CreateFromBackground();
bgSprite.Tint(r,g,b,s,l); // You'll have to supply these values;
// Now copy it back to the background
DrawingSurface* bgSurface = Room.GetDrawingSurfaceForBackground();
bgSurface.DrawImage(0, 0, bgSprite.Graphic);
// Clean up
Finally, you can also create a tinted version in Photoshop and draw that to the background in the same way (using bgSurface.DrawImage()), or by having it as a separate room background and changing the background frame.