Very interesting question. I have never been in a position that I have to search for this kind of software. But I did a quick search for you and I found a bit of information that may be of interest, I think.
This website offers a plugin for cPanel. The website builder is theirs but they give you a 20% for each site created with their tool (and it looks that, for your customers, it looks like it is your own site builder) http://breezi.com/cpanel-website-builder/
This other offer specialized website builders http://www.trendytools.com/cpanel-html5-website-builders.php
The third, a specific website builder software (which is, after all, what you asked for http://www.rvsitebuilder.com/home/installation/)
In this thread, they speak of another website builder that may be interesting and that you can host yourself http://www.webhostingtalk.com/showthread.php?t=461639
According to what they say, this website builder can have many additional features, such as powerful photo galleries or CRMs. I would read the whole thread but be warned that it is really old (2005)
This article mentions 5 different softwares that you can use and host yourself. the only thing is that it doesn't have a date so I don't know if it is current or not
I hope this helps you a little bit