By extrapolation from the official genealogical definitions of first cousins, second cousins, etc., siblings are 0'th cousins, aunts and uncles are 0'th cousins once removed in ascendancy (or removed upward), and nieces and nephews are 0'th cousins once removed in descendancy (or removed downward).
But zero'th cousins (or zero'th anything) is an awkward mouthful (I guess in England you'd call say zeddeth?). The parallel with "siblings", though, suggests the terms "uplings" and "downlings", which to my ear has a nicer ring than sibkids or rentkids.
You could even pretend that "sib" stood for "side", which would make a nice extension to up and down, but unfortunately it doesn't. According to etymological dictionaries, it derives simply from a term for meaning "kin" or "relative". A related word is "gossip", which originally indicated a godparent or godchild ("god kin"), and apparently acquired its current meaning on the basis of godparents gossiping about their godchildren, perhaps because godparents often served as matchmakers, or maybe because a gossip acts like they're everyone's godparent.
According to the Oxford English Dictionary, there is no official word in English for the term we're looking for, so I guess we can feel free to coin our own.
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