Does Tabular support custom tunings / can I use Tabular with my instrument?

Yes, Tabular allows you to configure a custom tuning when creating or editing a track (Document → Create Track / Command+T or Document → Edit Track / Command+Shift+T respectively on OS X). If your instrument has between 3 and 12 courses, and those strings are tuned somewhere between C0 and A5, you can create a tuning for that instrument. This means you can use alternate guitar tunings (drop D, downtuning, open tunings, etc.) or tunings for different instruments like ukulele, banjo, mandolin and so on.

Tunings can have either one or two strings per course, with some caveats. This setting is applied to the entire instrument as a whole rather than on a per-course basis, so you can't mix one- and two-stringed courses in the same instrument. You also can't configure the exact pitch of the secondary strings in each course. If the tuning of the primary string in the course is low enough, the secondary string will be tuned an octave higher, otherwise it will be tuned to the same pitch. These limitations will be removed in a future version of the app.

Note that Tabular currently does not support instruments with non-chromatic frets. This means that the difference in pitch between two frets is always one semitone, so certain instruments like the mountain dulcimer are not supported.