I'm managing a strategy that works very good for me. However, it depends on how many likes are you willing to get. So, the page I manage gets about 2k-3k Likes per week. It only takes you a little time to work on.
All you should do is constantly posting diferent kind of contests like: ''Here-s the prize (and a photo of the prize, for example a book). The rule of the contest obliges the contestants to like the page and share the photo.
Keep the contest rolling for about 2 days, then start another one, and another one and so on! When you finish a contest just copy the names of the contestants and paste them into a random picker site so you could pick a winner.
I really learned that a small prize can bring you a satisfying page likes number.
You could try it and see if it works well for you.