Pilots are demanding conventional SID rather than RNAV SID planned on flight plan due gps problem. In that case is it enough for a tower controller to coordinate the conventional SID with the approach unit or should pilots contact with their company to refill the flight plan?
The SID is normally assigned by the approach controller, not the scheduler, as SIDs are runway dependent and may change at a moment's notice with changing runways and because of noise abatement requirements.
A "default" SID is probably suggested by the airline's planning department based on historical patterns but there's no guarantee you'll actually get it.
If the SID you're actually getting doesn't match the rest of your flightplan, ATC will vector you. Just as ATC will give you instructions at any time they want you to do something that's not filed with them as your flightplan.
The airline has nothing to do with that, though they may want to know afterwards for their statistics and to explain possible extra fuel burn.
(In the U.S.) If you have already received your ATC clearance and then, while still on the ground, determine that you are unable to fly the assigned RNAV SID (due to aircraft GPS/navigation equipment problems) you should contact ATC Clearance Delivery (generally in the Tower) and advise them.
Clearance Delivery will then coordinate with the IFR controlling agency from which the clearance originated. Typically this would be an ARTCC unless it's a short range clearance within the Approach Control's airspace. Then the IFR controlling agency would provide a different clearance consistent with your capability to fly it.
It's possible that a different (conventional) SID/Departure Procedure would be assigned or a radar vector departure may be assigned.
Contacting your company dispatcher (or similar) to refile a flight plan should not be necessary under most circumstances that I can envision.
As a note for informational purposes only, here is a SID from Dallas-Fort Worth Intl (DFW) - GRABE EIGHT DEPARTURE (RNAV). It is comprised of two pages. Note that this same SID can be used for multiple runways. This, in the U.S., is very common.