This topic came up on Banjo-L and I thought I repost my reply here as this topic periodically comes up here too. Those who think anyone should be able to sing any song in any key may move on, this is about us un-extraordinary musicians singing with a banjo to back us up:
I too couldn't sing too many songs in G tuning, took me years to work out how to sing in the right pitch with the banjo because there were no explanations.
OK, here goes:
1) Find the lowest note you can comfortably sing. Then tune your FOURTH string to that note and tune the banjo from there.
A) How to find that lowest note you can sing? Take your G-tuned banjo and a common song like Red River Valley and a capo while ignoring the fifth string and find out which fret on the banjo you can most comfortably sing RRV. The notes you end up with is how your banjo should be tuned to fit your voice. Let us say you can sing RRV best at the 7th fret. That makes it the key of D and the strings are pitched ADF#A. Ditto for other frets and other pitches.
2) If you want to sing in the key of D and still have the G-tuning pattern, you have to get a short necked banjo, a long necked banjo, or thicker strings such as the Nylgut Minstrel strings.
Another thing and another tuning. In G-tuning Pattern, the key of RRV and many other songs is the third string but you need the lower fourth string to be able to sing the song. But in many songs you would not need that lower fourth string to be able to sing the song. Examples - Row Row your Boat, Hard Times (Foster), The Leaving of Liverpool. But here in such songs as The Leaving of Liverpool it forces you to go way up on that first string, perhaps beyond your vocal range. At this point I retune my banjo, still leaving that fourth string at the same note, but tune the banjo to the equivalent of what Tim Jumper in his Banjo Player's Song book calls "Graveyard Tuning" - aDF#AD which is an open D tuning. Then instead of using that 3d string to kick off/do the song, you use that low 4th as your starting/playing point. In the above example of the key of D dADF#A you would retune your banjo to dAC#EA for an open A tuning that still keeps that same low fourth string at the same note - A.
Maybe what I have written is about as clear as mud. The most important concept is finding what note your 4th string should be and go from there. I currently have a SAGA Pony banjo that I revamped and put light strings on and have it pitched to D (dADF#A) and a Ramsey that I have Minstrel Nylguts on tuned to E (eBEG#E). I wish I knew how to post audios or videos to demo all this but I am too computer illiterate. Maybe someone else can elucidate/demo what I am trying to convey. Best Wishes on your banjo journey! Banjered