The problem is that you cannot beat someone with nobody. This article talks about the race and Boner’s opponents:
http://www.theblaze.com/contributions/boehners-reelection-the-beginning-of-the-end/
Unfortunately it looks like Boner is going to win, particularly since there are three opponents and all it takes is getting the most votes to win. There is no runoff system if someone does not get more than 50%.
According to the article, the only hope is that Boner does poorly enough in the primary that a conservative will challenge him for the Speaker job. Not likely. If no big name Republican like Trey Gowdy will challenge Lindsey Graham for the Senate in South Carolina, I don’t think anyone with a chance to win will challenge Boner.
Sure you can just vote for his Democratic opponent, it would be a big improvement. He has to go one way or the other.