I'm not sure this is a bug or just terrible luck with the generating, however I'm starting to think it's the former.

In Capturing Wild Pet you get the screen showing where to place your catchers, and with a catographers guild I can now see where potential pets will be.

I only 'get' Gryphon, Cockatrice and Unicorns to show up. I've been waiting and waiting for a dragon or Roc to show up.
This has been going on for.. I don't even know how long. I thought it was a week, but then I checked the event log and I haven't seen or captured anything but these three since at least March 19th.
Last time I tried to capture something was march 25th, then I thought I'd wait.

I don't have anyone living at my inn to make this happen. The only invites I have cast are druid, dragon magician and I think it was a cartographer.

Browser: Chrome
OS: Windows7
I use two computers at different locations and neither of them yield differently.
I have tried clearing everything and doing the usual drill to see if it's just me.

If it is, that is some amount of bad luck.

You need to catch the pets that are out there in order to get different ones to show up. You said you haven't been catching anything recently so that's why nothing new is showing up.

Perhaps, but if you look at the log I used to capture pets. I've caught unicorns and cockatrice and they are still the only thing I can find.

As well as when I started the site I was looking around for Unicorns mostly and only found gryphons. But when I well found a unicorn without successfully catching one or anything else, they disappeared and were exchanged for gryphons.

However I will try to catch and see what happens.

I've had similar trouble, even posted about it before, but have just assumed it's the random generation and a coincidence rather than a bug.

I won't post my entire log, but since March 18th I've caught:
Cockatrice: 10
Dragon: 7
Gryphon: 4
Puma: 5
Roc: 1
Unicorn: 12

I'm actually having more diversity now than I was ever before. I think I've gotten no more than 5 rocs and 7 gryphons since I joined, easily more than 20 cockatrice and unicorns. Pumas and dragons tend to run the middle ground, neither rare or common.

The probability of different species spawning is the same. Please remember that flying pets spawn on the island, ruins and cave only. When you catch a non-flying pet, only another non-flyer can inhabit it's den.

You're saying I should capture Gryphons to get dragons and rocs?
So it is a must to capture pets for new to spawn, then.

I'll try, but so far it's looking like I'm only getting gryphons even so.

Asthora, yes, new pets are spawning only when you catch those who are already live in the dens of your manor. To get a probability of getting another flying pet, you need to catch the flying pets which are already on your map, otherwise the new flying pets won't have a free den to come. According to your log, you have 2 Gryphons taking layers, and you need to catch them to have a chance of other flying species to come.