Short answer: not really possible
<br>Long answer: possible, with extra work<br><br>
Currently, the only way to do that in OpenLP would be to define a custom formatting element that applies the correct CSS attributes to move a text block to the bottom of the screen. You'd have to manually insert that into every song you use, and you'd have to manually update each one to correctly name the next song. It would be easy to make mistakes with it and end up with undesirable results, but you could technically do it.