Ii ko imasse
Via languagehat, I learned of the World Loanword Database (WOLD). As the comments at the 'hat indicate, there may be room for discussion re the data (e.g. a bunch of proto-Malayo-Polynesian is in the donor list for Japanese — Ōno Susumu lives!), but there's still plenty to enjoy there. For example, the word danna 旦那, "husband, master, patron."
The immediate source of danna is Chinese tánnà 檀那. Chinese in turn borrowed it from Pali, where it was dāna दान and apparently meant "giving" or "generosity" in general — but, in the context of the Buddhism via which China imported it, the key meaning was alms.
The rest of the progression is obvious: from "alms" to "support for a temple" to "supporter of a temple" to "supporter in general" to a respectful term for someone at whose mercy your lifestyle is. And that's how Buddhist jargon provided the address term of choice for Kabukichō touts trying to lure drunken salarymen into establishments of ill repute. (Google results suggest that in the public consciousness, danna is roughly 50% as associated with this situation as shachō, "company president, [cas.] boss".)
language hat:
So danna is related to betray, perdition, rent, surrender, treason, vend, dose, antidote, condone, pardon, dowry, dacha, and Pandora. It all fits! (Isn't etymology fun?)