The closest I think are the furrie's conventions. They have some events going on at hotels that will go on for a weekend or so but I think we would have to make our own.
I would like to say that I'm not against the furry people and get along very well with tons of the babyfurrys I have met online but I will say a few things about my experience.
I went to one of the furrie's cons and hated it because if you didn't know anyone it's hard to make friends. Most of the people I was around were saying all of the internet memes the entire time. They would keep asking me which animal I was (I told them I was a puppy) and they asked why I didn't have a badge of my artwork on me.
It was fun to see some of the costumes and they even want you to have your photo taken with them and they don't mind you hugging them. Some of them are great but there are some others who smell really bad! I got business cards from a few of the nice people and they had tumblr accounts to see all of the neat pictures.
The other people who don't have the costumes still want to hug you. Most of these people were covered in sweat! They have a dance where they play techno music but most of the people there were obviously drugged up or drunk.
The few people that I did hang out with had some vendetta to tell everybody who was in the hotel (not just guests) that they were gay. I'm not straight but I find these people very selfish and offensive. They were telling random strangers (including myself) that they had a party room and anything goes.
I don't recommend attending the cons unless you're one of the furries. It's something they have fun doing and I went back to my room and put on regular clothes because they were making fun of my overalls. I was more upset because I got a cold on the last day there.
I will not attend another of the furrie's cons but If we had our own I would go.