Golarion has a Demon Lord named Xoveron, the Horned Prince, Lord of Gargoyles and Ruins. He doesn't have Domains listed, but Chaos, Destruction, Earth and Evil seem to make sense. In that setting, Xoveron appears to loathe cities and civilization, and want to bring them all to ruin, haunted only by his children.
White Wolf went another route, with a sorceress named Malgorzata being primarily responsible for the creation of the Gargoyles of that setting (which served the vampiric sorcerers of Clan Tremere, with the spilled blood and broken bodies of rival vampires used in the crafting). The Gargoyles worshipped her as their mother, and she doted on them as her children (to the point of fleeing with many of her children when ordered to destroy some).
Either take could be used to build up a Gargoyle god.
If they started as magical constructs, designed by wizards (or even priests), as guardians of the cities from aerial threats or nocturnal undead, they, like the elemental-spirit empowered Golems, might have broken free, and the God of the Gargoyles could be the first gargoyle to 'go berserk' and break free from the control of the spellcasters who had created and enslaved them. Freeing its fellow gargoyles from bondage, and somehow transforming from stony construct-nature to something brought to fleshly life by the elemental spirit trapped within (and thus being able to breed), this First Gargoyle would go on to become a demon lord or demigodling. Perverting their original lawful nature and purpose of guardianship and protection of the cities of men, they now want nothing so much as to tear down and destroy those same cities, embracing chaos and destruction.
They are too dim-witted to recognize that they still define themselves by the ancient shackles placed upon them, reactively doing the opposite of their original orders, rather than discovering any purpose of their own.
If going with the more Malgorzata route, the blood of vampires may have been used to bring these stony guardians to life, but incidentally also tainted them with a hunger for flesh and blood, and a chaotic evil nature that made them completely unsuited to their original intended purpose, as guardians and protectors of civilization and man.
