First thing - is it really true G minor, with notes of both Bb and Eb in the tune, or is it one of the modal minors such as G dorian or G mixolydian? These are sometimes written with two flats in the key signature, but don't actually have any notes of Eb in them. This may affect the keys you can transpose to.
Assuming that it is true G minor, and that you don't have accidentals: for the D/G box, the easiest keys to transpose to would be Bm (which you can get on the D row of your D/G box) or E minor (which you can get on the G row). The melodic range of the tune might affect which one you choose - e.g. if the tune in G goes up to top Cnat, you'll probably be stuck for the equivalent note in Bm (E nat). Similar considerations apply if the tune goes down very low and you're transposing to Em.
For the G/C, the equivalent keys would be E minor on the G row and A minor on the C row.
If the tune is in a minor mode rather than true G minor, or if you have a half-row of accidentals, you would have other choices.
Steve