The state of being cousins, the relationship of cousins(noun)
Wiktionary.org : Text is available under the Creative Commons Attribution-ShareAlike License
Use "cousinship" in a sentence
"But among the Moslem tribes, I am told, female cousinship is not recognised."
"Any other kind of cousinship can be so elusive and distant that by itself it tells us very little about a relationship, even if it could be established."
"John's "cousinship" afforded an excellent basis for informal companionship, and Clementine gave it full prominence."