You can take a train from Kars to Yerevan via Akyaka, Bayandur, and Sasunci David in around 10 h 1 min.
How to get from Kars to Yerevan
From Kars drive to Aragats then Electric train to Yerevan. 7 h 15 min $64. From Kars train to Akyaka, drive to Bayandur, Electric train to Sasunci David, then subway to Anrapetucjan Hraparak. 10 h 1 min $66. From Kars drive to Yerevan. 6 h 13 min $72.