One guy would keep cash in a hidden pocket in his suitcase and if customs gave him trouble he'd politely inform them about the pocket they didn't check and everything would get resolved.
Another guy would be bringing in parts for his company and when things got held up he'd talk to the person of the appropriate rank and offer to pay the "expedited" fee to get things through, as these were very important pieces of equipment. There was no expedited fee.
Somebody else would literally just sneak them cash as they shook the custom officer's hand, but they had a working relationship and knew each other on a first name basis.
One person got pissed off and refused to pay a bride and literally just waited until they changed shifts and his stuff was released.
If sincere, congratulations.