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 "$@"
Recently, the Pale Moon team also forked Gecko, as Goanna. Currently Goanna is used in the beta builds of Pale Moon.
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