Bloody Mary (SAMAMIYA Akaza)

Set in Yokohama, this is the story of a vampire with a death wish and a priest with a "survival wish."

After hundreds of years, Mary - an immortal vampire who wants nothing more than to go to his final rest in peace - manages to discover the whereabouts of Maria, a legendary exorcist who has "Maria's Blood," which can be used to kill immortals, running through his veins.

However, this particular Maria is merely a descendent, and is himself clueless about vampire hunting. Despite that, having inherited Maria's Blood means he's constantly being targeted by vampires. Mary thus makes a deal with Maria: in exchange for Maria's discovering a way to kill him, he will protect him from those who're after his life.

Note: This manga is not BL.