I once heard a song that had two diminished chords in it, which probably has something to do with Modal Interchange, it's just I've never encountered it before. When I heard this song it sounded really good, so how can I use it on my own?
The concept of modal interchange (or "modal borrowing" or "mode mixture") is that you "borrow" a chord quality that is diatonic in the parallel key. If you're in, say, C major, you can borrow chords that are diatonic to C minor (and vice versa).
So to find opportunities to borrow diminished triads, let's first find where those diminished triads are. In major, it only exists as vii°. And in minor, it exists both as vii° and as ii°.
Since both major and minor have the same vii° chord, you can't really borrow one into the other. But there is one remaining diminished triad: ii° in minor. Thus, from a standpoint of modal interchange, the only other way to introduce a diminished triad is by using ii° in a major key.
The same logic applies for the seventh chords. In major, the seventh chord on scale-degree 7 is half diminished; in minor, it's half diminished when built on scale-degree 2 and fully diminished when built on scale-degree 7.
There are other ways to introduce diminished harmonies, especially with secondary leading-tone chords (vii°/x). But in terms of strict modal interchange, this is the only way.