If you need to find one in a hurry, phone the local hospital
who will have a list, or telephone these numbers depending on the town and get
the list in English.
2018 Update.
I have just phoned the Larnaca number to make sure it is
valid.
(There is a charge per minute which is specified to begin
when the announcement of that charge ends.)
You will also find the information affixed to the door of
any chemist, with a list of who is open and the address out of hours for
that period.