API-650, Appendix-P covers only nozzles at the bottom of the Tank, "The recommendations of this appendix represent accepted practice for the design of shell openings in the lower half of the bottom shell course that have a minimum elevation from the tank bottom and meet the requirements of Table 3-6."
How do I calculate the stiffnesses of the nozzles at the conical roof of any API-650 Tank?

Obviously nothing to do with API 650.

Either use Roark or a small finite element model to establish stiffness.