Faux wood paint effects - dry brush light colour on dark for dark wood, dark colour on light for light wood. See painting miniatures page for faux techniques
Use Wood Finish Stain Markers to stain small pieces. Your local Home Depot, Lowe's, Ace Hardware, or Sherwin-Williams store can order this product in for you upon request if they do not have them on their shelves.
Nontoxic wood stains can be found in your kitchen - see this article.
Another staining alternative - fuming, which involves placing raw wood pieces on a rack in a large barrel above a container of ammonia, and covering the barrel tightly. The pieces are rearranged occasionally, until the desired shade is achieved. Use a Mason jar laid on its' side with a small jar lid inside holding the ammonia and a piece of old screening held above the lid by some Lego pieces as a rack to support the wood above the ammonia. It took sheet basswood and craft sticks three days to reach a lovely deep golden brown, but only two days for the dowels, coffee stir sticks, toothpicks, matchsticks and poplar chopsticks, and less than 24 hours for a length of 1/4" square balsa. It is far slower than staining, but there's no stain under and around my fingernails or all over the workspace, I have real control over the final results and it costs perhaps 2 or 3 cents per batch. Or it could have been completely free.