Your best bet for part time work is to go look at air freight/air freight forwarder type companies. ie Bax/Schenker, Ceva Global, even DHL, UPS Supply Chain. Fedex Ground/Home delivery and many others that I cannot think of or don't know about.
You will need your own authority, if you have a cargo van and are thinking about this you might try going down to the airport area, most of these type companies are near an airport and talking to the terminal or operation manager. Also check with the local courier type companies. i'd even get some business cards printed up with your company name "Acme expedite" LOL
Pass out ten or so to each of the businesses you visit and then they can put them up on their bulletin boards at their desks, that way you will always be on their mind.
You will need to do research on price to charge etc. I'm not the one to ask as far as getting your own authority etc. Just giving you some ideas to think about