Yes, it's possible for both players to play using one keyboard. To do that, you must select "Use keyboard" in player 1 and player 2 control option. Then remap keys so that player 1 would use WASD to move and player 2 would use arrow keys for example.
Be aware of button limit though - in some setups the keyboard only registers up to 4 button presses at a time.
If you have no controllers I recommend using Player 1 - Keyboard and Player 2 - Mouse.