A recipe? The traditional one goes like this, add 2,5% of salt to the weight of the meat, and some sugar. Cure in the fridge for three days or more, the thicker the meat slab the longer the cure. For very thick pieces of meat, you would like to find some veins and inject salt water into the veins.
Regarding your nitrite/migraine relative he/she should consider giving up a very bad habit. Namely swallowing your own spit, because it contains much more nitirites than it is normally possible to get from food. He/she should also stop eating several of the quite common vegetables.
I think it is almost impossible to get the artificial red color on the meat without using nitrites, celeery juice or the salt. If you for some reason want to stay away from nitrites, you just have to sacrifice the red color. And the slight change of taste.