I would go the opposite way. Get rid of Counterspell as a spell.
Instead, allow appropriate spells (either the same spell or something else that the DM feels would work) to be used to counter other spells. For example, you could attempt to counterspell Fireball with either your own knowledge of Fireball or Control Flame.
Of course, this would require being able to recognize the spell being cast so that you could choose an appropriate spell. For that, you could treat it like a passive perception check that is based upon Arcana. Then there would be some sort of opposed roll.
"Counterspell" then becomes a feat (Improved Counterspell) instead of a spell:
"Improved Counterspell - add +1 to your choice of INT, WIS, or CHA; if you did not already have proficiency Arcana, you gain proficiency and may choose to base your passive Arcana on your choice of INT, WIS, or CHA; you have advantage on opposed caster checks for the purposes of counterspell."