How do I replace a 3-way switch on 2-wire cable with a programmable timer switch?
You'll have to purchase a timer that is specifically designed to work as a 3-way switch. Or you'll have to rewire the other 3-way switch in such a way that it will no longer control anything. 

Since I can't see the wiring at the second switch, I'm guessing the wiring currently looks something like this...



Which is sketchy, since there's no grounded (neutral) conductor running with the travelers. It's not clear where the grounded (neutral) conductor that the light is connected to comes from, so you'll want to look into that.

To get this timer working, you'll have to bypass the other 3-way switch like this.



Again, I don't know what the whole circuit looks like, since you've only offered a partial look. So I'm guessing at the wiring when it comes to the second switch.