The Ancient Macedonian word κοῖος
Word κοῖος
k o î o ς
IPA koîoς
Meaning number
See also Homeric Greek: ποσός ‘of a certain quantity’
Proto-Indo-European: *kʷóti~kʷéti ‘how much/many’

According to Athenaeus Deipnosophists it is the Macedonian word for number. Probably from proto-Greek *kwotjos (later posos), deriving from PIE *kwoti 'how much/many'.

If that is the case then the following happened to *kwotjos:
  1. loss of intervocalic (and initial) /s/ -> *kwosios became *kwoios
  2. the labiovelar *kw normally gives /p/ in Greek, but in in some dialects it can result /k/ e.g κότε instead for πότε, ίκκος instead of ίππος.

Based on the above κοῖος should not be compared to standard Greek αριθμός but to ποσότης 'quantity'.

Another etymological suggestion is that it is related to the verb κοέω to observe, learn, hear, estimate, take to account’.

Beekes (2014) considers the possibility of the word being an Anatolian or Pre-Greek loan.

See Hoffmann (1906), Kalleris (1954) and Filos (2015).