Protaras and it's surrounding areas all within the municipality of Paralimni have available for hire transportation of various sorts.
Apart from the obvious Taxis and Long Taxis as well as those mini-buses you can also, for those special occasions, hire out Limousine Taxis and/or Limousines too, often refered to as Limos.
It may be for a simple Wedding to take the Bride and Groom to and from Church where you might take a proper Limousine, or it may be a Limousine taxi to take you and your friends out for a big birthday party, maybe a 21st, 30th or 50th birthday or even a Wedding Anniversary for you and your loved one where you may prefer a proper Limousine. There are even persons who want to take their friends (or partner) out in style for no special reason at all except to make it special.
As for details of where to find such a Limousine for your needs you can either search via the web beforehand if you are staying at private accommodation, check with your hotel or your tour operator representative during your stay anywhere in Ayia Napa or Ayia Thekla who will surely have the details or able to find details for Limo hire.
For that special occasion or to make an occasion special there is always that something else available.