I would be surprised if there are any reliable phone apps- for one, you're going to have cues that are late if someone's service is bad. You can also use cheap walkie talkies, but they are really not well suited for this.
Have you considered using cue lights? It's pretty inexpensive to create a simple cue light system- all you need is a box with some light switches, cable, and some small bulbs (you can use Christmas tree bulbs, which are small and easy to hide on a set). An electrician can wire up a simple system. It's standard practice to put 2 bulbs on every switch, right next to each other, so that if one burns out, there's always a backup.
If your theatre is looking to purchase a system, you might see if a larger theatre in the area is upgrading their comm system and looking to sell their old one. Or, look into renting a system.