Consider running a Facebook "Like" campaign. It's very targeted and Facebook actually helps you optimize it. Then, once one of your ad versions gets more and better results for lower cost, keep that ad version, stop the others, and start another ad to see if you can beat the first one.
Keep repeating that process until you get likes for 10 cents or less apiece, and then increase your budget for the best performing ad with the lowest cost until you either reach the desired number of likes or until the likes become more expensive again.
It's a terrifically effective way to increase likes quickly, but it does cost quite a bit, especially if you want several thousand likes. Still, it's cheaper than almost any other ad types on FB, at least from what I've seen.
Also, be sure to make your page likable by posting some great content, and target your ads towards the kind of content you provide. After all, the visitors you attracted with your ads will still need to "like" your page, and they won't do that unless they actually like it ;-) Of course, that's probably obvious.
Hope this helps! Good luck!