You seem to have the wrong assumptions.

“Royal” and “loyal” are adjectives derived from nouns. “Noyau” is a noun derived from a word that was an adjective in Latin. And no parallelism can be drawn in the origin and history of those words.
An adjective noyal from the noun “noyau” would not conform to the logic of the French language.

“Royal” derives from latin regalis and loyal from latin legalis. The derivation from rex and lex was done in latin before the words existed in French, so no law can be inferred about all French nouns ending in “oi” having adjectives derived from them ending in “al”.

“Noyau” is a noun that happens to end with au in the singular. This “au” ending of the noun has nothing to do with the rule that says that in French most adjectives (but not all, lots of exceptions) ending with “al” in the singular will end with “aux” in the plural.
There’s no such noun as noyal, and there’s never been. The only occurrence of “Noyal” in French is for some place names in Brittany^*.
And this « noyal » is said to come from Latin novale or novalium designating some recently cleared piece of land.

The noun “noyau” comes from Late Latin adjective nucalis itself derived from latin nux (→”noix”). Nucalis meant “having the size of a nut”. The adjective nucalis and its diminutive nucleus gave old French noiel→noiaux that gave the noun noyau (1530) to designate the stone of a fruit.

It started being used in a figurative sense in the 16th century.

Two adjectives are derived from “noyau”. “Nucléaire” and “nucléal”, they’re roughly synonyms (but a scientist might explain a difference in use), nucléaire being by far and large the most used.

^{* Which could lead us to think the name could be of Celtic origin.}

Pour noyale le TLF donne : “Toile de chanvre écrue très résistante, utilisée autrefois pour la confection des voiles des navires. Noyales à quatre, à six fils (Ac. 1835, 1878).”… et le correcteur d’orthographe ne le connait pas. Conclusion : l’oreille francophone du XXI^e siècle ignore ce mot.

Les multiples influences subies par les mots ne permettent pas de dériver une loi de quelques exemples.

Laure vous donne une explication grammaticale, mais intuitivement un noyau n’a pas de comportement humain, donc, bien que vivant il ne peut être noyal, d’autant plus qu’il est caché ; la notion de noyau s’est d’abord rattachée au fruit.

C’est la science qui a apporté le terme nucléaire, qui, sauf erreur de ma part, n’est pas employé dans l’arboriculture.

Pour l’homme on emploie parfois le mot cœur pour renvoyer au noyau de son être, mais noyau et nucléaire ne renvoient pas aux mêmes imaginaires.