It feels rather reassuring that after going through red pigments, all but two that I have found so far are actually poisonous. Most of the other ones are still in use today. But still, please note that even if a pigment is considered safe, there is still a possibility to get an allergic reaction to it.
Alkanet root Cold, or blue-toned red pigment coming from a plant, Dyer's bugloss Considered safe and is used today as colourants both in makeup and food.
Brazilwood Warm red pigment coming from wood of Caesalpina brasiliensis. Safe, but the tree is considered an endangered species. Substitute with Red sandalwood.
Carmine, Cochineal Bright red pigment that comes from the scales of the cochineal, an insect. Considered safe and is used today as colourants both in makeup and food.
Field Gromwell, Corn Gromwell, Bastard Alkanet Carl von Linné writes in 1755 that peasant girls in the northern parts of Sweden uses the root for red makeup.
Litharge, Red lead Red pigment made of lead. Poisonous, so even if you could get it, don't try it. Red pigments from Iron oxides can be used instead.
Red sandalwood, Red sanders Red pigment coming from the root of the tree of the same wood. Used in makeup today. Similar to Vermilion in colour, but fades quickly.
Saffron A very expensive spice that colours everything you use it in bright yellow. However, saffron was also used for Safflower in the 18th century. Safflowers can yield both yellow and red pigment, Carthamin. It seems quite likely that saffron in recipes for red makeup really means Carthamin. It is used today as food colourant under the name of Natural Red 26.
Vermilion, Cinnabar A red pigment made of mercury. Poisonous, so even if you could get it, don't try it. Was known to be dangerous in the 18th century but was still used. Substitute with Red sandalwood.