.. dye or paint ?? ..

Dye is paint its just lacquer based and more flexible when dry. Either applied from a spray can will make carpet feel like scotch bright pad under bare feet just because it takes so much of it to cover. A little fabric softener brushed in helps.
A fabric dye ( RIT brand ? ) might be a better choice.
I've done lots of carpet repairing and spot dying with spray cans on used cars but not in my A-body.