You need to be able to show some evidence of a basis for the painting, which would typically be the fair market value on the date of the death of the decedent (from whom you inherited the painting).
You might be able to get some sort of back-dated appraisal from an expert in the field. Beyond that, however, you would have to use a basis of $0 if you cannot find some reasonable method of determining the FMV on the date of death.