What about diabolic dragons?
As other answers have explained, a character can easily have both diabolic and draconic ancestry from different ancestral lines. But a character could also have diabolic and draconic ancestry from the same line.
Abishai for 5th edition are found in Mordenkainen's Tome of Foes and are antagonists in Baldur's Gate: Descent into Avernus. They are draconic devils. They have the creature type of Fiend (Devil) and speak Infernal, and have all of the resistances of lesser devils. But they also speak Draconic, appear physically like humanoid dragons (with wings and claw / bite attacks). They come in five colors to match the five types of evil dragons and have immunity to one damage type that matches their color. They are followers and worshippers of Tiamat, a great diabolic dragon who was once the ruler of Avernus, the first layer of the Hells, and are currently "outside the infernal hierarchy".
Previous editions gave them draconic scales, although duller than those of true metallic dragons, and called them the "purest children of Tiamat" - it was clear that Tiamat created them by promoting lemures.
As far as I can tell, 5e lore has not yet established whether they are actually diabolic dragons or draconic devils or whether it is possible for them to sire children with humanoids, and whether such children would be considered to have both draconic and Infernal bloodlines. It would not be a great stretch to make it so for any DM so inclined. If so, it would be possible for someone with a single Abishai ancestor to be a Tiefling sorcerer with the Draconic bloodline. Or, for that matter, a Dragonborn sorcerer with the Infernal bloodline.