It seems like the diminished chord (vii° in major, ii° in minor) is not used as much in modern popular music compared to classical music and the remaining chords of the diatonic scale. Is it actually rare?
The half-diminished (or m7b5) is usually suggested as the diatonic chord on the 7th degree in major keys and the 2nd degree in minor keys, and is fairly common in most styles of music.
Given that in any key there are basically (diatonically) three major chords, three minor chords and only one diminished, and that diminished doesn't stand alone, or constitute a key on its own, statistically, there's a one in seven chance of any random diminished chord being used, whereas a three in seven (nearly 50:50 ) of a chord being major or minor.
Most songs seem to get away with not using what is quite an unusual chord - in several ways - as there are plenty of other options which will suffice. However, a lot of showtunes use diminisheds, and they can be made to fit into quite a few existing tunes with no great effort - and can sound good as replacements.
I guess it depends on what exactly you mean by 'modern popular music'. Generic pop music has a general formula that it rarely deviates from. Jazz has lots of seventh chords and that could easily count as modern popular music, a number of these chords are diminished.
It will all depend on the effect you want to create, the diminished chord has an uneasy feel to it. rather pretty but you are going to want to have to use that effect.
Here is an example of a song that I'm pretty sure ends on a diminished chord, used rather beautifully. It does have its place.