Are you mental!? Persephone can't have any demigod children cause if she did, Hades would be pissed and kill them, the same reason Hera can't have any demigod children

Persephone had a child with Zeus ^.^
...and it's only because Hera is the goddess of marriage. She has hinted that she wants demigod children sometimes. :P
Aphrodite has children with Ares and mortals, but Hephaestus hardly does anything about it.
Hades couldn't really 'kill' them, because gods can't do anything to heroes, unless challenged. :D
I think it's quite possible that she has 'flings' in the six months when she's not in the underworld. xD
Poseidon had a child, and no one knew that he did, until he claimed him. So, it's not likely Hades would find out until she claims them, which she doesn't do because she has no cabin for them. Just a suggestion. XD

In the end of 'The Last Olympian', they build loads of cabins. For his gifts from the gods, Percy says 'And the minor gods, Nemesis, Hecate, Morpheus, Janus, Hebe - they all deserve a place at camp half blood'. The - shows that he didnt have time to say all the minor gods but he means all of them. So maybe Persephone does have a cabin at CHB, or not. We'll never know.

Don't know, depends on what she does with her time when she's not in the Underworld.

She's loyal to Hades, like Amphitrite is to Poseidon and Hera is to Zeus. She wouldn't have kids with anyone but him.

...but... she had a child with Zeus... xD