In order, I'd go with
Ruby,
Pearl, and then
Garnet as well. For me, I'd probably name
Jasper's sister as
Amethyst, if using another gem name.
Though, I also enjoy these combinations:
Jasper and
FloraJasper and
MavisJasper and
AdellaJasper and
NadiaJasper and
CelestinaJasper and
Miranda