The Counter Skill is indeed one of the most dangerous skills an enemy can possess, but it does have weaknesses that can be leveraged. Here are four methods I found, that can be used to "counter a Counter". The methods are sorted by relevance.
Counter does not work on ranged attacks. It will work on magic, if your unit is attacking from an adjacent tile, though. Therefore, the best way to counter Counter, is to attack from afar. Whichever weapon you use to achieve that, does not matter.
Counter works only against non-lethal attacks. Meaning: If the enemy has 80 HP, and you deal 80 damage or more, you will not suffer from Counter. Consequently, Lethality is your best skill against Counter, albeit somewhat risky to use, since there is no way to predict its activation (unless by abusing the RNG).
Be extra careful against enemies who also possess the skill: Miracle or Pavise or Aegis or any other skill that may reduce the amount of damage received.
It is also recommended to avoid using this method with units, that have the Astra skill, as Astra halves the damage done and thus maximizes the damage received from Counter (the Astra bow is fine though, as it is a ranged weapon).
This method relies on the use of recovery, in order to offset the terror that is the Counter skill. Obviously, having a good healer in the back is going to help a lot against Counters, but that is only if you manage to survive it. Also, when fighting many Counter users, you'll need either many healers, or a healer with Fortify or the Goddess Staff.
Alternatively, you may offset the damage received from a Counter with the skills: Sol, Aether or Lifetaker (though Lifetaker is useful only during your own turn). Alternatively to the Sol skill, there's also the Sol sword.
Nosferatu and Aversa's Night are especially useful against Counter, as they can not only be used to snipe, but also to recover some of the health lost on Counter, as the healing effect of those weapons is guaranteed to activate.
Counter doesn't work against Dual Attacks, so one of the safest ways to defeat an enemy who Counters, is to attack him with a unit, that does little to no damage and who is being supported by a unit that does a lot of damage. Both units preferably have a high support level with each other, in order to increase the odds of launching the "Dual" Attack.
This is likely the least relevant method to use, as most characters that could survive fighting a Counter user, will also have a high enough Str/Mag to deal significant damage, even when equipping the weakest weapons available. Also, the amount of units that can make use of this method, is going to steadily decrease, as your units grow stronger.