How do I add a apt-get repository without editing /etc/apt/sources.list?

You can place files in /etc/apt/sources.list.d. This is described in the man page for sources.list (type man sources.list). The man page says:

Older SOURCES.LIST.D

The /etc/apt/sources.list.d directory provides a way to add sources.list entries in separate files. The format is the same as for the regular sources.list file. File names need to end with .list and may only contain letters (a-z and A-Z), digits (0-9), underscore (_), hyphen (-) and period (.) characters. Otherwise they will be silently ignored.

UPDATE:

2016 SOURCES.LIST.D

The /etc/apt/sources.list.d directory provides a way to add sources.list entries in separate files. Two different file formats are allowed as described in the next two sections. Filenames need to have either the extension .list or .sources depending on the contained format. The filenames may only contain letters (a-z and A-Z), digits (0-9), underscore (_), hyphen (-) and period (.) characters. Otherwise APT will print a notice that it has ignored a file, unless that file matches a pattern in the Dir::Ignore-Files-Silently configuration list - in which case it will be silently ignored.

You could try:

add-apt-repository <REPOSITORY LINE>

The repository line would just be what you would append to the sources.list or a PPA repository. Check out the manpage here, or execute:

man add-apt-repository