Have a suspicious old man/cocky young kid or whatever offer you the location of a sure-fire get rich quick ore deposit in the system as a rare rumor encounter in the Trafalgar Pub and other locations with rumors (slums, statiomaster's offices, etc) (regardless of whether there *is* a deposit). The player then has to pay them a smallish fee (maybe 500cr base, increasing with level/size that is claimed?), at which point they get a nav marker. This tipoff may or may not actually contain ore, but there's enough chance that going for rumors is better than blind searching when you know there's deposits in the system.
Might even be worth creating a deposit for this mission so that even if the mines are convinced there's nothing, you can still sometimes get lucky.
In addition to the chance the that the tipoff is a lie, there should also be a separate chance that the suspicious old man sold the rumor to a bunch other miners who would already be at the tipoff spot trying to find ore when you get there.