I used two pens, both wooden (they won't damage it, even if they can), one foundation and it has to be 3 walls high (a few somehow glitched up and over 2 walls). The pens I made are 5 foundations apart, and was able to pet the lower level pupper. Make sure after you've dropped it with your flying mount (I used a pteranodon) you move your mount away from the pens. If it's close to it the hyena will just try and run around. Once you've crouched and petted it, it should stay in the same spot. Keep waiting and petting and you're done.
*I had a doorway with no door for the pens, they don't go through doorways.
Normally you can't tame the pack leader, so just get a pteranodon or argy, pick it up and drop it in a large area (like a separate section of your base). When you take it away from the rest of the pack, it removes its 'pack leader' title, allowing you to tame the highest level hyena of that pack.