The name is fairly long, and are people really looking for a standalone billing system. It should be part of the ERP or whatever system they decide to use and thus a selection criterion. But it doesn't look like something you can easily plug in.
For a payment processor, that is another story.
I haven't checked the search volume, you never know. Not hopeless, but tough sell.
The previous holder is Buydomains, they gave up on this after 4 years.
PS: automatedbillingsystems.com is available.