On a peer to peer network, you must configure them to share files in order to use any kind of centralized backup solution. You just need to determine what kind of device and media you wish to use, and go from there. Device and media choice would be determined by the approximate size of the backup jobs and speed requirements - and whether you want to store backups offsite (recommended). If you wish to do offsite storage, CD-R is most economical and convenient if the daily jobs will be less than about 1 gigabyte, otherwise, it's hard to beat good old tape backup. If you are satisfied with onsite storage only, a hard drive would be fine, either external USB/Firewire or internal in one machine.
This is a very reasonably priced software package for what you need.
http://www.stompsoft.com/bump/
This can essentially automate the job.
Edit: A DVD burner would be an attractive option, even an inexpensive single layer disk can hold at least 5 gigs of compressed data and you could even use rewritables to keep the media cost down - put the media on a rotation schedule and erase them.