Once sure of the amount of powder that the pistol can SAFELY shoot. And I stress SAFELY as the weapon design is often based on the capabilities of the powder it is meant to shoot... I can not see something with that short of a barrel shooting any large amount of powder.
But to obtain the top performance, if percussion cap, I would shoot 3f Triple Seven powder. If flintlock I would shoot 3f Swiss black powder. Remember these were belly guns. Made to be used at extremely close quarters. Most of them only produced around 450 ft per second ballistics as I once read.
A friend of mine once owned a derringer, very much as you described. I will not say I recall the load he used. But the powder amount was very low. What amazed me was the penetration of that ball at close ranges when he shot it. He shot into bundled magazines. And I never thought it would penetrate as deep as it did.