By their nature compost piles work better the larger they are, so you aren't likely to get very quick results from a small pile, although they do still work.
If you are going to be composting mostly vegetable scraps, coffee grounds, and paper products, look into a worm bin (worm inn is a good one for your situation). They take up very little space, fairly easy to maintain, and will break down your waste much faster than a simple compost pile of the same size.