I introduce the Magneto-Nuclear Periodic Table (MNPT), a pedagogical and predictive framework for electron-free nuclear matter (here termed nucleomorphs). In this regime, electrons are absent by design and stability is governed by nuclear composition and magnetic confinement rather than by electronic shells. The MNPT organizes hypothetical and semi-physical species into families driven by magnetic moment, spin alignment, and confinement topology. I formulate a Magneto-Nuclear Stability Index that combines magnetic, structural, and mass-to-charge terms to score the plausibility of a nucleomorph under given fields. The framework yields a finite initial table (34 entries) to teach the concept and guide computation and lab trials. I document predicted applications (energy, shielding, quantum memory, propulsion) and provide synthetic routes (natural extraction or laboratory formation). An extended Appendix defines requested symbols (BKP, BKH, NDS, NDL, ART, ARG, ARN… including coded states like ART(3 0 6 0)), giving each a meaning, proposed use, and proposed method of obtaining. This work is hypothesis-driven; experimental confirmation is an open challenge.