Okay, this is the last bunch. I don’t think we name any other relatives besides these.
Cousin showed up in the mid twelfth century, from the Old French cosin, which besides meaning cousin, also meant nephew or a relative in general. Further back it’s the classical Latin consobrinus, a weirdly cool looking word that just means cousin. Like uncle and aunt being specific to a particular parent’s side of the family, consobrinus was too, originally just meaning your mother’s sister’s son (and no, I don’t know what the other ones are). Man, they sure were specific in Latin. Also, you can go a bit further into the etymology. Consobrinus is a mix of com- (it switched to n), meaning together, and sobrinus, another Latin word for cousin, again, specific to cousins on the mother’s side (though slightly less specific than mother’s sister’s son). Plus sobrinus comes from soror, sister (as in, sorority). The TL;DR here is: cousin is a combination of the prefix com- and the word sister.
Niece showed up in the early fourteenth century, from the Old French niece/niepce, and classical Latin neptia, which actually means granddaughter. In fact, until the early seventeenth century, we actually used niece to mean granddaughter or another distant female descendent. Interestingly, there was another word used for niece before niece: the Old English nift. That word comes from the Proto Germanic neftiz.
Nephew showed up at the same time as niece, in the early fourteenth century. It also comes from Old French, in this case neveu, grandson, and before that the classical Latin nepotem (if that looks familiar, it’s because it’s the origin word for nepotism). Nepotem means grandson—neptia is actually the feminized version of it—and it also was used more broadly until the seventeenth century. Plus, before we used the Latin version, we used the Old English nefa.
Finally, I’m going to talk about the prefixes grand- and great-, but only as they relate to relatives (ha!). People started using grand to mean someone of an older generation in about the thirteenth century. Anglo French started the trend that would give us grandparent (they started using graund dame for grandmother), but Latin and Greek were doing the same thing, so you can’t really say they invented it. It’s similar with great, although it wasn’t in common use until the early fifteenth century, and it was basically a transliteration of what other languages were using to describe older relatives.
So that’s it for relatives. Did you have fun?
Tony Jebson’s page on the Origins of Old English