There is a list of music software maintained at linux-sound.org. It's pretty exhaustive, you might want to poke through that list and see if you can't find what you're looking for:
It looks like Lilypond can do what you want. The notation also goes by the name "Simple Notation" and also "Ziffersystem".
If you look towards the bottom of the references section of the Wikipedia page you referenced there are links to Lilypond specifically about this notation as well.
After googling a bit more I found this Q&A over on the SE site music.stackexchange.com that asks the same question.
This notation is also called Jianpu. There is an extensive reference to Jianpu here on this blog: BennyT85Erhu's Blog.
I found this feature request from 2011 to have JianPu support added to the application Musescore. There is a list of applications that do support JianPu in a post on that feature request.
It would appear that musescore is working to add this as a feature to their application. It's listed here on the 2013 page of projects and has someone assigned to work on it.
Jianpu notation support in MuseScore
Jianpu notation/Numbered musical notation is widely used in China. A
large amount of Chinese music is recorded in Jianpu and most Chinese
people are more familiar with Jianpu than standard staff scores. But
there are relatively limited software for editing Jianpu and they have
obvious disadvantages. In sum, there's a need for high quality Jianpu
notation software. For more information: Here.
Student: Eli Yang
Possible mentor: lasconic, Rui Fan (aka Vanferry)