As I recall, Diablos is pretty challenging when you first get him if you haven't been doing any grinding or excessive magic-drawing early on.
The key to the fight is the spells that you can draw from him. He always carries Demi, and will have either Cure, Cura or Curaga depending on his (i.e. your) level. Draw these and use them to your advantage.
The Demi spell instantly removes 25% of the target's current HP. This means you want to draw it and cast it as your first couple moves. The more HP he has, the harder it hits. In this way, you can drop him to half health in two shots.
From there, beat him down with standard attacks and magic. As a flying monster, he is weak to Wind. Make liberal use of the Cure-family spells you can draw from him.
His Gravija spell hits extremely hard, but it works the same as Demi, it just takes a much higher percentage of your health. If he puts you into position for a Limit Break, you can also do a lot of damage that way. (Remember, you can hit the Circle button to retry for a Limit Break if you're at low HP).
Finally, don't be afraid to use any healing items you have. Items are plentiful in FFVIII, and you'll be able to easily resupply later on.
Quoting this post on the Steam Community is about the best answer I could find.
What I do is I use an Xbox 360 controller with Pinnacle Game Profile (but any other software like this should do the trick).
First I go to My Documents\Square Enix\FFVIII Steam\ and there's the ff8input.cfg. Open it with Notepad, then under "Joystick" replace every value with 0, so gamepad is completely deactivated.
Then I use a Pinnacle profile where I map A button pad to A keyboard, B to B, X to X, Y to Y, LB to L and RB to R. The rest is not that important so map as you see fit. Once it's done I remap the keyboard in the launcher with the profile I made. Be warned, game is based on QWERTY so if you use AZERTY, A is Q. So once in-game, I will have the good input prompt (in my case, B for confirm, A for cancel, X for playing card, Y for menu, R for gunblade trigger / rotate camera right, L for rotate camera left). Pretty useful for Zell tricks.
Best Answer
You can farm the Elnoyle in Esthar City or Tri-Faces as per this post