A "Shotgun" is dispersing projectiles right from the muzzle and this limits the effective range due to big dispersion and lack of accuracy at bigger ranges. We have programable munitions like 40mm ATOM which I think are better suited for this job.
Shotgun would be a perfect last option solution for a soldier on foot for a self defence against drones, but I think there are better ways in which we could use the base and the resource of a vehicle than a shotgun if we talk about a dedicated counter-drone vehicle. We may be able to intercept the drone in question far away from the effective range of the shotgun.
There is also another important thing to note when it comes to combating drones. The further you intercept it, the better. This comes from the fact that the drone may not explode in the air, but instead it may fall due to the damage done to its control surfaces while the warhead is still active. This means that if you intercept the drone close to you (or the intended target of the drone) the chance of it just slightly departing from its course and hitting close enough to its target and cause damage is big. The drone must preferably be intercepted far away from anything important it can damage with its warhead.
I think Aselsan SARP-Dual can be a very good solution and it can also act against ground threads with its programmable 40mm ATOM and other weapon of choice.
SARP-Dual firing ATOM 40mm programmable munition:
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If we want to pump things even more we have Aselsan Serdar which can be configured for an AA role after a few tweaks.
The whole configuration may look close to the one of the Coyote, but a bit less complicated as it would be an all around solution:
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Aselsan Serdar:
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As far as I remember we have a launcher that we developed and is compatible with both SUNGUR and CIRIT so it may be configured accordingly.