One of the best ways to promote a pet site is by adding it to gaming directories and promoting it on gaming forums.
This approach can help you attract new members and support both short-term and long-term growth, especially through directories like Topwebgames, Apexwebgames, pbbg.com - Persistent Browser Based Games
Creating dedicated social media pages for your game can also be an effective way to promote your pet site. Be sure to post images and screenshots of your game to engage potential players.
I’d also recommend writing about your game on platforms like Medium and HubPages so you can spread the word to a broader audience. Pinterest is another excellent tool for promotion—you can pin images and link directly to your pet site.
Another great tactic is to engage with specific subreddits on Reddit that allow weekly promotion threads. You can showcase your game in these threads to reach new audiences.
For example, the IndieDev subreddit is particularly helpful for indie game developers. https://www.reddit.com/r/IndieDev/s/2mlyQfWumx
Lastly, another method that can help promote a pet site is by releasing a press release, which is a very strong marketing tactic as it can gather a lot of media attention for your pet site.
In my opinion, the best way to build a pet site is to get involve in the target community. Then, you need to enable authorized users to share their pets and breed their pets too. That way, it will be easier to gain more users.