There are other demonyms in literature, but their validity is uncertain (as it was proved by the fact that you could not find more in the dictionary).
Neptuniano as a demonym of Neptuno is, apart from the reference in Alicia's answer, present in wiktionary
Neptuniano: Originario, relativo a, o propio de el planeta Neptuno.
Interestingly, the DRAE gives this word a different meaning, that has little to do
Dicho de un terreno o de una roca: De formación sedimentaria.
Similarly wiktionary's "plutoniano1/-a: del planeta Plutón" has a complete different meaning in DRAE
Perteneciente o relativo al plutonismo (vulcanismo).
Conjunto de fenómenos relacionados con los volcanes y su actividad.
Teoría que atribuye la formación del globo a la acción del fuego interior.
And "uránico/-a (uranita): del planeta Urano" has another problem. Uránico is not present in the DRAE, and neither uranita, which is a uranium-rich radioactive mineral (thus the name).
Wiktionary includes in its entry for_gentilicios_ "solar" as
solar: 1. del Sol - 2. del Sistema Solar
which again is technically not true by the DRAE (DRAE says for solar that is relative to the Sun as a star, not to the Solar system).
Wikipedia also has its own list, but the article is unfortunately not available in Spanish. This list includes
- Earth: Earthling, Terran, Terrestrial, Tellurian, Earthian
- Jupiter: Jovian
- Mars: Martian
- Mercury: Mercurian, Hermean
- Neptune: Neptunian
- Saturn: Saturnian
- Uranus: Uranian
- Venus: Venusian, Cytherean, Vesuvian
but if you were to translate or adapt Neptunian as neptuniano and Uranian as uranio you'd run into the problems described above: the dictionary does not include these terms with such meanings.
1. While the dwarf planet Pluto can be out of the list according to the "Great Planet Debate" I decided to include it in this answer to illustrate the difference between literature about the demonyms and their validity according to DRAE.