A few months ago I discovered a very efficient way to increase the amount of followers ("likers") of the Facebook pages of my clients. It requires systematic manual work but it's worth the effort.
It can be summed up in a few words: always invite users who reacted to your Facebook posts. When people like (love & other positive reactions) your posts (either editorial or promotional), simply click (on desktop) on the row of reactions, select "ALL" (to get all types of reactions in a single list) and start inviting all the users who reacted to your post (beware: exclude negative reactions).
You'll be amazed at the amount of "page likes" you'll quickly get from this recurring process.
I usually dedicate a few minutes per day to go through the latest posts of my clients and hit "invite" on all the new reactions. A labour of love ;-)