What defines a "deep cut" is very subjective, differing from person to person, but Urban Dictionary gives the definition

A song by an artist that only true fans of said artist will enjoy/know. True gems that are found later in an album, a b-side. Rarely if ever played on the radio.

Generally, these songs are from rock-style (including folky like Mumford and Sons, blues, alt-rock, etc.) or contemporary bands and even solo musicians, ranging from anything around the '60s to the present day. Pretty much look at what's posted and get a feel for it. Keep in mind nothing is necessarily disallowed, but if you think there's a better place for it, it probably belongs there.

If you aren't sure where to look for other music, check out /r/music for more genres!