is a prefix of Latin origin, and is used to form words that include the meaning ‘together, in common’. Spelling practice varies with regard to use of a hyphen: some words (especially when the second element begins with a vowel) include it, whereas others are written as one word. The diaeresis (ö) that formerly punctuated words as in coöperate, is now largely disused. Recommended spellings are as follows:
coagulate / cofactor / co-opt
coalition / cogeneration / coordinate
co-author (noun and verb) / cohabit / co-parent
cohere / co-partner
coaxial / co-host / co-pilot
co-determination / coincide / co-respondent (in divorce case)
co-driver / coition
co-education / co-latitude / co-signatory (to an agreement etc.)
coefficient / co-occur
coequal / co-occurrence / co-star
coeval / co-op / co-worker
coexist / cooperate / uncooperative
coexistent / cooperation / uncoordinated
coextensive / cooperative

Modern English usage. 2014.