Before you go ahead and spend time and money, consider this. If your measurements are accurate, and you have true 2x10 joists spaced 16 inches on center, and they are old growth wood, you may have lumber with an F allowable of approximately 1500 psi. This can only be verified by a hands on review by an individual qualified to grade old lumber, however 1500 psi is not uncommon.
If your lumber is 1500 psi, and using 40 psf as the load on the floor above the joists (you need to verify with your local code enforcement official what the required load is for your location, however 40 psf is not uncommon for bedrooms), your joists at 19 foot span would have a factor of safety against bending failure of approximately 1.8, a maximum deflection of about 3/4 inch at midspan, and a d/L of approximately 350.
The 3/4 inch deflection is totally normal for a beam, they are going to deflect downward due to the floor load. You noted in your post that the deflection was approximately 1/2 inch, which is consistent with this analysis.
Based on this, you may want to reconsider the need for the project. The joists do not appear to be undersized, and the deflection is normal. Small deflections such as you appear to have should not have any impact on flooring. If you find the bounce of the floor objectionable, that is a different matter. There are other less expensive techniques than sistering to reduce bounce.
I recommend you hire a qualified structural engineer with experience in evaluating the properties of old lumber to take a look, and offer an opinion as to the structural capacity of your joists. You may be surprised to find that they are good the way they are.