You could use a programmable remote control with a built-in timer. The Sony one (link below) lets you program up to 8 different timers. I'm sure there are others out there that aren't quite as expensive, but I have one like this and I know it works well.
But, I'd consider something else instead of multiple DVD players, a switch box (for the A/V signals), and a programmable remote. I'd use a small computer and store the video on the hard drive (a DVD is about 5 GB, so most drives today will hold many DVDs). No switch box is required, and the computer OS probably has a simple event timer that can run a DVD player with a new file name. I presume you aren't trying to play copyrighted movies, so you'd have full access to the video material to store on the hard drive.
You could optimize the computer for your video needs and even have it networked (if you want) to allow for online updates. By the time you get 4 DVD players, 4 sets of cables, a programmable switch box, and a programmable remote, you're pretty close to the cost of a cheap computer. You'd have a lot fewer failure points with a computer, and if you networked them, you'd have a lot less labor costs (no driving out to change out the DVDs). Optical drives fail with dirt and dust; no dirt or dust can get into sealed hard drives. Quantity buys of the same configuration from the same mfgr can reduce the computer costs as well...