In terms of potential based on other users feats of the lesser powered gravity rod (the cosmic converter belt is supposed to be above the og gravity rod and the staff above it and more recent star rods) Courtney has the possibility to take it. Based purely on her feats alone she looses.
Ted Knight using the earlier gravity rod was able to beat earth 3 Ultraman, the OG rods power also empowered the stallat entity Aquarious to be able to solo the JLA and JSA. In all star comics Sylvester stated his OG CCB was above that OG rod.
Sylvester used the OG gravity rod to defeat Vulcan sonnet fire. In the same story Vulcan shattered Alan Scot constructs and broke Classic Fate spells.
The problem is that only a single showing of Courney's alluded to the same level of power. When her and Powergirl were fighting ancient gods said gods were more concerned by Courtney's access to "cosmic power" than PGs.
The only other thing that came close was when Courntey's cosmic rod broke thru the energy Shield of Obsidian around the brownstone. A shield that had already held up against Alan blasts from within and the attempts of the souls from Hiroshima bombing to breach from without (same souls Crispus Allen Spectre couldn't contain next issue alone). Though this breach was after said souls touched the rod and possibly amped it and after she had absorbed the entire cities electricity grid.
Jack Knight also used the rod against some pretty powerful entities under Robinson.
In short, if we feat shared Courtney has a small shot, based solely on her feats not