Honestly, I'm not much into Christian fiction because it's very preachy, and usually hokey or just plain wrong. (Left Behind series comes to mind.)
That said, I know some, but it depends on your definition of "action."
And, if it helps any, since I do write fiction that probably does show there is a Christian behind the writing, (I am not a Christian writer, I am a Christian who writes), I deal with violence the old-fashioned way. Suggest it, instead of vividly show it.
My MC did join a full battlefield battle, but instead of showing the carnage, he had just enough time to notice strategies his side was taking to deal with the enemies, before he was pinned down by the enemy. He can't see himself being bitten, (the enemy was a dog pack), and then he passed out so he missed everything but the ending. (When he woke up, he was being pulled away in a wagon, but still had time to see the outcome of who won and how.)
That's about it, suggest it, instead of show it. Or pick a story that has no violence in it. (Charlotte's Web and Ghetto Cowboy come to mind, but neither are "Christian stories." Still, both have action.)