The train runs from Tbilisi on odd days of the month and from Yerevan on even ones.
From the official timetable of Georgian Railways.
There is a train #202/201 Tbilisi – Yerevan which leaves at 8:20pm and arrives 7am. This train leaves Tbilisi on odd dates such as was yesterday and when you have 31 days in a month skips the 1st. This train will go back the next day such today leaving Yerevan at 10 pm and arriving to Tbilisi at 9 am
EDITED
There is a schedule if you can Google Translate it from Russian. It states that train to Tbilisi arrives at 9am. There is no indication from the page that this train doesn’t run every day. So it is quite likely that it is.
Credit:stackoverflow.com‘