Try this:
Write the order of flats:
B E A D G C F
See if it works for you.
For Sharps go to 4 to the Right, For Flats, go 3 to the Left
So if we are at F maj, and want to determine it's relative minor
go four to the right and you have d
but if you want F# major's relative minor, go to F# and go 3 to the left
Bb, go to four,eadg G (just don't think of this one as a flat)
Eb, go four to riight, adgc, C minor
Ab go to Ab count from there 4 , DGCF, F minor
Db, go four to right - gcfb, and then you have bb, relative minor
Gb go four to right , CFBE, EB minor
Cb go four to right, FBEA, (you just make it a flata0 Ab
You just have to have your major key signatures memorized in order to do this.
I saw someone do this another way with the modes, but can't remember how,
If anyone knows, please let me know.
I hope this helps