It is not normally possible to book a taxi in Granada.

Almost all taxis in Granada are controled by one company.
The number is 958 280 654

You phone and you are asked your destination.
The operator then finds the nearest taxi to you
once the operator has found a taxi for you you are told the number
of the taxi that will pick you up by a automated voice then you are cut off.

If they can't find you a taxi they will just cut you off

The problem is that if you don't speak Spanish you may not realise that
your call for a taxi failed.

So, if a taxi does not arrive within 5 minutes phone again.

The only way to book a taxi is to arrange it directly with a taxi driver.
So, if you are coming to Granada for the weekend and you come from the airport.
Ask the same taxi driver to pick you up for the return journey.