Rewiring digital clocks to make them run faast? (eg- make 24 hours go by in 24 minutes)

Not really. The levels of integration are too high to allow any user modification.

Have you checked out Grainger for the parts you need?

http://www.grainger.com/Grainger/wwg/start.shtml?cm_mmc=PPC%3a%20Google-TPN%20%20Brand-Grainger_-grainger

My first hunch would be “not really”—they usually use some sort of hard-wired oscillator, though you might be able to read chip numbers off, Google up a datasheet, change a resistor value somewhere, and fix it up.

Much easier, though, would be to just make your own circuit. If you’re willing to buy and take apart a sprinkler timer, why not do the same thing for not a lot of money with a 555 timer and a mechanical relay? Here’s a link as an example.