A self-healing dielectric elastomer is achieved by the incorporation of metal-ligand coordination as cross-linking sites in nonpolar polydimethylsiloxane (PDMS) polymers. The ligand is 2,2'-bipyridine-5,5'-dicarboxylic amide, while the metal salts investigated here are Fe(2+) and Zn(2+) with various counteranions. The kinetically labile coordination between Zn(2+) and bipyridine endows the polymer fast self-healing ability at ambient condition. When integrated into organic field-effect transistors (OFETs) as gate dielectrics, transistors with FeCl2 and ZnCl2 salts cross-linked PDMS exhibited increased dielectric constants compared to PDMS and demonstrated hysteresis-free transfer characteristics, owing to the low ion conductivity in PDMS and the strong columbic interaction between metal cations and the small Cl(-) anions which can prevent mobile anions drifting under gate bias. Fully stretchable transistors with FeCl2-PDMS dielectrics were fabricated and exhibited ideal transfer characteristics. The gate leakage current remained low even after 1000 cycles at 100% strain. The mechanical robustness and stable electrical performance proved its suitability for applications in stretchable electronics. On the other hand, transistors with gate dielectrics containing large-sized anions (BF4(-), ClO4(-), CF3SO3(-)) displayed prominent hysteresis due to mobile anions drifting under gate bias voltage. This work provides insights on future design of self-healing stretchable dielectric materials based on metal-ligand cross-linked polymers.