Would cortisone shots be helpful for weak hair growth?

Facial hair is a genetic trait that you inherited from your parents. It is a secondary male characteristic trait that shows with the onset of puberty. You can't grow more facial hair with medications or supplements. The only way to add more facial hair is a hair transplant surgery.

I would strongly not recommend cortisone injections for thin beard hair.  Cortisone injections are used to treat hair loss that is caused by your body attacking the hair follicles such as alopecia areata.  

Cortisone is only an option if you have one diagnosis in particular: alopecia areata. Please see a dermatologist if you're not sure. Facial hair is strongly genetic. Options are limited, although some of my patients have used minoxidil, platelet rich plasma in addition to hair transplantation. Cortisone won't help unless you have alopecia areata. Experimenting can be unsafe as there are side effects with steroid injections that one best stay away from unless they are treating alopecia areata. 

Cortisone shots will not cause you to grow mustache or beard hair.  If you are missing hair there, it could be genetic and can be fixed with a transplant