By far the best way to have your routers on the correct time is to have them sync up with an NTP server.
Basically, you designate one or two hosts or routers as ntp servers on your net and have them pull time from public stratum 2 servers on the internet, and then set your other routers to pull time from these local ntp servers. If you have Unix boxes or a Win2000 domain, you might already have local ntp servers to use. Go to:
http://www.eecis.udel.edu/~ntp/
.. for everything you need to know about setting up ntp servers.
I know most Cisco routers do not have a clock chip like a PC does. I don't think the 3600 or 2600 series does either.
Greg