And then is it C Cm Bm E7 Am D G or something?
pretty much. for your Cmin, put the bass to Eb, and for your Bm, make it Bmin7, and for your E7, make it E7sus4 (maybe just Esus4), and for your Am, make it Amin7, and for your D, make it Dsus4, and then it's in good shape