Ich dachte, ihr könntet mir eventuell sagen, was ich wissen muss.

Would the meaning of “eventuell” allow for this translation? “I though you could potentially tell me what I need to know.”

I would say yes.
The meaning of “eventuell” ranges from “maybe” over “possibly” to “conceivably” and “potentially”.
Another possible (albeit verbose) translation is “I thought you might happen to be able to tell me what I need to know”.

German synonyms include “vielleicht” and “möglicherweise”.