It is very possible that Nuva ring has coused the rash.
Acctually, there is a list of penile disorders due to contact with Nuva ring substances.
Rash on the penis is far more common reported side effect, than bruised penis, scraped penis, irritation on penis, cracks with bleeding on head of penis, penile irritation after sexual intercourse, painful penis after intercourse, dermatitis (inflammation) on penis and scrotum.
Try to avoid sexual intercourse for a period and see if his rash disappear (that will be a proof for allergic reaction to the Nuva ring).