Somewhat ironically, I'm going to go with an answer that meets half your criteria.
Half Magic, by Edward Eager, the first book in the Tales of Magic series.
Four children wish on a Half Magic coin that gets their mother Alison half-way home, rescued by Mr Smith. Mark's wish zaps them to a desert without island, where half-talking cat Carrie gabbles to a camel. Romantic Katherine battles Launcelot. Eldest Jane rejects siblings for another family. Stubborn youngest, Martha, causes a riot downtown.
A black, green and white cover with a girl on the front with a sword and helmet. Check.
It DOES have Carrie the cat in it, however her colour is never given. Nor does she drink a purple drink.