More difficult to do without preserved soft tissues.
Maybe the teeth, marrow, or growth plates on the femur could have detectable traces of any contagion.
But mostly any disease would have to be inferred from changes to the bones themselves as in the case of syphilis causing deformations.
Hoping the tech improves enough to make it vastly easier.
Teeth are the #1 carrier of ancient DNA and contagion, but the 1918 Spanish Flu samples had lots of available sample: skin, bone, teeth etc.