I am not sure if you were aware, but this article is about ISPs and we currently have laws that already regulate them and make the behavior described in the article as illegal.
So yes we do regulate them. And these laws are called common carrier laws. And those have have existed for decades and uncontroversial, and yes they work.
> Are there any regulations which both sides could be happy with
Both sides are indeed already happy with our existing common carrier laws that apply to ISPs, yes. Common carrier laws are not controversial.
What's not so clear to me is whether (A) the allegations against the ISP have any merit (the article itself states it has no confirmation), or (B) even if they were true that they would run afoul of the common carrier laws. As far as I understand, these regulations do not prohibit the carriers from selectively promoting (and, ipso facto, selectively suppressing) the content they carry.
Indeed, how could it be otherwise? The capacity of the carrier is always going to be finite, therefore, tough choices are always going to have to be made as to who gets priority access.
Civil rights legislation can happily co-exist with a "no shirt, no shoes, no service" sign on the shop door.
We already have many laws that effect companies.
For example, power companies cannot just turn off your electricity because they don't like what you say.
These are called common carrier laws and they are completely uncontroversial.
We live in a society, and it is perfectly OK for us to put limits on what major monopoly type companies can do.