It appears that D&D made up King Orys I for the show. The wikia page on Orys I has this to say about the character:
As Elio Garcia of Westros.org, co-author of the World of Ice and Fire sourcebook explained, this was also not simply a matter of Charles Dance (Tywin) mispronouncing a name, because he had seen the broadcast script, and it clearly said "Orys the First" (the on-screen subtitles also spell this name the same way). Garcia stated that Benioff and Weiss had apparently just invented this "Orys the First" and he doesn't correspond to any character from the books. In order to reconcile this, Garcia said that this "Orys the First" should probably be interpreted as just a king of the independent Kingdom of the Stormlands, from long before the Targaryen Conquest - in which case he was not one of the established Targaryen kings but a local king of House Durrandon. This would make his full name "Orys I Durrandon". Tywin therefore wasn't citing him as a king who sat on the Iron Throne, but an infamous example of a (local) king, remembered over three centuries later for how his own brother murdered him. Garcia also pointed out that "Orys" was not a common name used in the Stormlands until after Orys Baratheon became their new ruler during the Targaryen Conquest.
However, as far as I can see all of this information is gathered from the following quote and no others:
Having seen the broadcast script, D&D invented a King Orys. Fairly sure he's intended to be a Storm King, though of course the name Orys is not originally from the stormlands.
Don't worry, Oberyn's daughters are safe.
Therefore the full quote from the wikia seems to be making guesses as to who Orys I is. As far as we know he was some Storm King though again that is only a guess but at least it is by Elio.
The previous quote states that the script stated Orys and not Aerys. Both transcripts I was able to find also state Orys I:
A good king must be just. Orys I was just. Everyone applauded his reforms.
Springfield! Springfield!
And:
TYWIN: Yeah. A good king must be just. Orys I was just. Everyone applauded his reforms. Nobles and commoners alike. But he wasn't just for long. He was murdered in his sleep
after less than a year by his own brother. Was that truly just of him? To abandon his subjects to an evil that he was too gullible to recognize?
Genius