Paint can be a good substitute, but you want to be careful with what kinds you use, fabric paint can work well but you want to make sure not to apply it too thick or else with use it can crackle and peel off. It can last for a while or only one con depending on the wear and tear you put on the costume. Another painting option could be making stencils and lightly spray painting the color onto the fabric, it works well with cotton blends but not more plastic-y materials like polyester.
Also I have a friend that I am helping make a vault suit as well and we are hand sewing the numbers/stripes on and even though i only know one stitch, which is a really rough stitch, I feel like the inconsistent stitching really helps to fit the worn out fallout vibe. Just an idea, stitching can be a pain but the end result is usually really cool and lasts a while!