Playing upright is a good choice as is wearing a strap, so you can be more relaxed, less concerned about holding the autoharp steady or not dropping it.
Slider is both a type of strap and a brand. There is a special size for autoharp (short). I suggest buying it from Autoharp Quarterly. See
http://www.autoharpquarterly.com.
If you enlarge it, the picture at the top of this page shows strap buttons attached to the face of the instrument. One is at the uppermost tuning pin. The other is a the lower left below the chord bars. There are other possibilities for locations but these work and are the same classic locations once used by the US factory for the Centurion and Appalachian models, the only ones with strap buttons included.
You may find that some of the excess leather needs to be cut away from the end tabs of the strap. That will allow more easily attaching the strap in a cramped space.