Quick answer: not easiliy.
Your requirement #1 is in opposition to the others.
Let's look at a counter example. #1 requires the changes to be imperceptible to humans. That means you cannot add to, take away from, or modify the visible image. For starters, that opens the "analog hole", where a photo of the screen masks the watermark data.
Requirement #3 says it needs to be robust. Developing a scheme to remove or obscure a watermark today is done in two ways. You can compare a watermarked file to an original in hopes of deriving a way to reverse every change made by the watermarking process, allowing the attacker to write a tool to "unsign" the images.
But that's not the only valid attack. The attacker can compare two watermarked files against each other. Remember, the attacker doesn't need to remove the watermark data to be successful. All he has to do is introduce enough doubt that you can't prove if the file came from the image distributed to client A or the image distributed to client B. In a courtroom, the content producer is suing client A for copyright infringement, but he can only collect from A if he can conclusively prove it came from A and not B. (The success rate of this attack grows even further when the attacker incorporates more watermarked copies than just two.)
If I could issue visibly different media to A and B, then the info could not be removed so easily. Let's say it's an animated video where I have a scene with a background shelf cluttered with household stuff. I can render it with a blue teapot in video A, and a red vase in video B, and repeat this concept in as many scenes as necessary to help with #5. (The same concept could perhaps be done with a percussion instrument in a music track.) Any copy will uniquely identify the two, but requirement #1 says they cannot be perceptibly different.