Update: here is a sample 360 video I took with the Guru 360.
As of Q1 2017, there are a few gimbals designed specifically for 360 cameras. Two of them (NS VR and Wenpod) are designed for heavier 360 cameras and for camera rigs and cost about $2,000. The first affordable 360 gimbal is the Guru 360 by GimbalGuru.
I had the chance to try it out. Here it is in action!
As I mentioned in the video, I'm going to test it out further this weekend. Stay tuned for a more detailed analysis and some sample 360 videos with the Guru 360. And if you have particular questions or requests, please post them in the comments and I'll do my best to address them. Please note this is a preproduction model, so the final specs and appearance are subject to change. Please note also that there's an app for it that enables it to be controlled remotely but I don't have access to that app yet.
In the meantime, if you preorder the Guru 360 from GimbalGuru.com, you can get a significant discount.
BTW if you found this post helpful, I would really appreciate it if you can share it with your friends! Thank you very much! (Note: I didn't get the Guru 360 for free. I ordered it myself for the same price as everyone else after seeing the demo videos they posted. This unit is just being loaned to me for early access.)
Update: I've now had the chance to use the Guru 360 for a 360 video. Here is a sample 360 video I took with the Guru 360.