What do you call a unit of beer within a pack?

What's wrong with beer?

There are 12 beers in a 12-pack. The price is 70¢ a beer.

In the UK trade this is sometimes referred to as a "single". Usually meaning one bottle from a case of 6, 12 etc, where the case is the main stock keeping unit (SKU) for distribution. It could also apply to cans.

E.g. "Quantity: 3 cases, 1 single." or "Quantity: 1 cases, 3 singles."

You'll see this reported on customs and excise forms along with liquid volume and alcohol volume and other tax related measures of quantity.

Serving makes sense:

a single portion of food or drink; helping

I would use can, and the first time you do this, explain that everything you say equally applies to bottles and you're using the term can for simplicity.