Banana Republic was a term made for Honduras when the USA Fruit companies (main export: Bananas) and CIA were the ones running the country behind the scenes and democracy was only theoretical.
Based on this, yes Cyprus was made a Banana Republic with the 1960 agreements. Instead of having the people democratically creating their constitution, the foreigners forced their own rules that included things like "Guarantor powers", huge military bases etc. A true Republic would of course never have such things forced on it.
However what I find ridiculous, is that Bananiot is making this thread. If what we have now is Banana Republic once, what would have been created with the Annan plan would have been Banana Republic 100 times. I am not even sure if Banana Republic would be a term good enough, maybe Joke Fake Republic would be a better term.