They don't want it to go into a bank account or they don't want to give you their actual bank details to facilitate the transaction?
If you know and trust this person, it will take them no time at all to set up a Paypal account so you can send them the money as 'friends and family' rather than as you would an ebay transaction, the former is free, the latter has an associated charge.
There are probably other solutions like Western Union, but I imagine there's a charge involved with that too. I suppose the ideal solution depends on the amount, exactly what method they will co-operate with and whether you are willing to pay for the transaction.
Of course, if you want it to be totally off the radar, you could post them the cash. If it's well disguised and you use first class post, it will probably get there the next day, but if it gets lost or stolen in the post, the money is gone.
Or you could use Special Delivery and it is very likely to get there the next day, and it will be insured if it doesn't (I think) but that costs a bit more.