The Dwarven language was created by Aulë when he created the Dwarves themselves, and called it 'Khuzdul', which simply meant 'Dwarvish'. The language was harsh sounding, and sounded strange to other peoples. No person who was not a Dwarf was permitted to learn any of its words, for it was guarded jealously. When around other races, the Dwarves seldom spoke in Khuzdul.
Certainly in the First Age when they first made contact with the Elves, the only tongue in Beleriand would have been Sindarin, as the Ñoldor had not yet returned from Aman. As a logical consequence, Sindarin was a language used by the Dwarves. In fact, they were so impressed by the Elvish runes (the Cirth of Daeron) for writing Sindarin that they adopted them for use in their own tongue, and used them forever more.
