As far as I'm aware, line stations in general don't hold pitot covers in stores unless their station is one designated as at risk from insects. If the a/c are scheduled to nightstop for any length of time at an 'at risk' station then provision will be made either to place pitot covers on board (noted as a tech log entry ADD/HIL/DDR etc) or to have the pitot covers shipped to the line station for the duration of the schedule.
If the a/c diverts to a non normal destination then a suitable local engineering MRO would be tasked with the job, and one would assume that if that station is on the 'at risk' list then they would have pitot covers in stock anyway... one would hope.
On the other hand, as happened last summer, every aircraft had to have the pitot heads inspected and signed off in the tech log within two hours of first flight of the day instead of fitting the pitot covers. (i think that was for scheduled ground time of less than 24 hrs and may have only been short haul. IE A320).
I think the pitot covers are type specific with an approved part number.
On the other hand there are some airlines that insist on pitot covers being fitted anytime they are on the ground for more than a few hours regardless of the local insect threat.