does japan allow citizens to date their first cousins?

There's no law out ruling marriage between cousins in Japan as far as I know.

There's no law in any country that says you can't DATE them (well, maybe in Arab countries?). Yes, marriage is legal too in Japan, China, and Europe - in fact, it was rather common amongst the nobility in 19th century Europe. But whether or not it's genetically desirable is another matter: due to the limited gene pool, the risk of having a child with congenital disorders is higher.

Regarding the post below mine, I live in the UK now and I've lived in the US before... I am not aware of any differences in the interpretation of "first cousins". The children of your parents' siblings are your "first cousins" whether you live in Alaska or the British Antarctic Survey Research Station.

Personally, I find my own cousins to be repulsive little brats.

Please define first cousin. The "first cousin" in Britain and America differ.
If you mean cousin (e.g. the child of your farther's sister.) you can marry with her/him in Japan.

they do it..maybe we should too he he