I was reading the description of sickening radiance and was wondering if there were any other ways to give another creature levels of exhaustion in combat? It seems like it could be very DM dependent.
At the time of writing this I can find no character or monster ability (in the PHB, DMG, MM or XGtE) besides the spell you mention that directly causes exhaustion. There are two indirect, but canonical ways that could work in the timescale of a combat:
The fastest way to gain exhaustion listed in the DMG is to sprint:
During the chase, a participant can freely use the Dash action a number of times equal to 3 + its Constitution modifier. Each additional Dash action it takes during the chase requires the creature to succeed on a DC 10 Constitution check at the end of its turn or gain one level of exhaustion. (p.252)
So if you give them reason to run and then chase them, you can indirectly cause them to gain exhaustion.
There is at least one feature that causes the user to gain exhaustion, the frenzied rage of the barbarian. If you dominate such a creature (eg. with the spell dominate person), you can cause them to use the feature and thus force exhaustion upon them.