The song in question can be found here. For example:
いっぽんでもニンジン
While I do know that でも means 'but', I also know that most particles have multiple meanings.
Since 'but' wouldn't make much sense as a translation here, I am confident that でも is used here to mean something else. That's what my question is about.
What does the sentence structure ＡでもＢ mean as it is used in the song?
The でも in the song is conditional/hypothetical "even if" (indicating 逆接の仮定条件), rather than the conjunction (接続詞) でも, "but", which usually comes at the beginning of a sentence.
The でも here consists of で (the continuative form (連用形) of the copula だ) + binding particle も.
So 「AでもB（だ/です）」 means "(It's) B, even if it's A."
１本でもニンジン lit. (It's) ninjin, even if one.
→ It's called [ni]{2}njin, even if there's one piece (of carrot).２足でもサンダル lit. (They're) sandaru, even if two pairs.
→ You call them [san]{3}daru, even if you've got two pairs (of sandals).
Examples of this でも:
- 雨でも行きます。 I'll go even if it's rainy.
- 難しい仕事でもやります。 I'll do even if it's a difficult task.
- ２個100円。３個でも100円。 Two for 100 yen. It'd still be 100 yen even if you bought three.
The song is meant to teach kids counter words. In every number from 1 to 10, there is an example of a number + counter for that kind of concept, then でも, and then the actual word that needs the counter that was used.
If you look at the example word given for each number+counter word carefully, you will notice that it resembles the next number.
- 一本{いっぽん} でも にんじん
- 二足{にそく} でも サンダル
and so on.
So I don't see why でも couldn't mean "but". The actual meaning is vague, though, because the song doesn't have a real grammatical structure. It's just a list of amount+でも+item.
Some possible interpretations of the function of でも here:
