For a month now my boyfriend has had these lumps around his penis, they are hard and don't pop. What can they be?

Be seen. He should be seen. If you have any new bumps or lumps you should be too. They could be benign, but could also be an infection.
Penile cysts. If by "around" you are referring to the base of the peenis and scrotum, then they are probably benign cysts. Since this portion of the anatomy is of some importance, it should be evaluated by his dermatologist!
See md. These could be sexually transmitted disease , so ot is best to have them checked for your own protection. They can also represent benign growths which amy require a biopsy to confirm.