Two people, one keyboard: rules that prevent the argument
Agree on the key order before the deal, and stop while both still want a round.
Two-player play on a single keyboard breaks for exactly three reasons: both people pressing at once, nobody knowing whose turn it is, and a results screen too small for both to read. Every other argument is a consequence of those three. Agree on one detail before starting: who presses during whose turn. Any game that lets both players steer at once without turn order will always end in a tug-of-war over the keyboard.
Pick games with a clean split screen or a clearly marked turn swap. If the score sits in tiny type in the top corner, the loser will doubt the number, and doubt is bait for one more round, then another. A good two-player game prints its score large, colours each player's turn differently, and ends on a short verdict instead of a chart.
The last rule matters most: stop while both of you still want one more round. An extra round played after one player is tired leaves a bad taste, while stopping on time gets the keyboard invited back tomorrow. Twenty minutes is plenty for a shared session; the rest of the lunch hour belongs to other things.

Candy Chain Master
Number Domination