Is there such a thing as peritoneal cancer?

YES: It is known as ~ primary peritoneal carcinoma. Now there are other cancers that can start in the peritoneum like mesothelioma and others that can spread to the peritoneum like gastric, colon and ovarian to name a few. When this happens its described as peritoneal carcinomatosis.

Yes: As rare as it may be when it does occur is is usually as a result of metastasis from another primary cancer. Ovarian cancer can arise and present with peritoneal spread but colon and bowel cancer may as well. Additionally, some lymphoma may present this way. Basically though any advanced aggressive cancer can spread to the peritoneum with some more common than others.