A root in The Etymologies of the 1930s glossed “crow”, with derivatives ᴹQ. korko and N. corch of the same meaning; it replaced a root ᴹ√KARKA with derivatives ᴹQ. karka and N. carach (Ety/KARKA). The deleted form conflicted with contemporaneous ᴹ√KARAK “sharp fang, spike, tooth” (Ety/KARAK). This deleted form nevertheless may be connected to S. crebain from The Lord of the Rings (LotR/285), whose singular craban “bird of crow-kind” (PE17/37) might be derived from ✱k(a)rak-wan.
There is another primitive form ✶k(a)wāk used as the basis for “crow” in the Quendi and Eldar of 1959-60 (WJ/395), but even later this primitive form was the basis for Q. quácë “frog” (VT47/36); see the entry on √KAWAK for discussion. As a result, I think earlier ᴹ√KORKA is probably the best choice for “crow” words for the purpose of Neo-Eldarin.
This root appeared in The Etymologies of the 1930s glossed “red” (Ety/KARÁN), a later iteration of ᴱ√KṚN of the Qenya Lexicon of the 1910s of the same meaning, but with syllabic ṛ (QL/48). Its main Quenya derivative, Q. carnë, retained the same form throughout Tolkien’s life, but its Gnomish forms G. carn(in) “scarlet” and G. crintha “rosy, pink” (GL/25, 27) became N. caran “red” in the 1930s, and retained that form thereafter.