Originally Posted by Palal

Look at the calendar - you have days starting from 1 to 28, 30 or 31. About or exactly half of them are odd, the other half are even.

Railway Timetable (Georgian Railways)
timetable Armenian railways

So it looks like Yerevan-Tbilisi runs on even days, and Tbilisi-Yerevan on odd days. Don't expect to get much sleep on this train, as you'll have to go through the border and you'll get woken up twice.

There are also minibuses that take 4-5 hrs, and according to a 2013 posting on this forum leave from the bus station every hour starting at 8AM, and you can always get a private car there as well (I assume they'll take less time).