Conkeror does work (more or less) with Pale Moon browser [ https://www.palemoon.org/ ], which forked from Firefox 24, and maintains the XUL framework.
To run Conkeror with Pale Moon, use the following command (and/or alter your .desktop files or alter /usr/bin/conkeror accordingly):
palemoon --app /usr/share/conkeror/application.ini "$@"
To make Conkeror work with versions of Pale Moon which use Goanna rather than Gecko, change /usr/share/conkeror/application.ini by adding the following lines (if not already present) after the [Gecko] section:
[Goanna] MinVersion=1.9.1 MaxVersion=9.9.9