I have shipped a pair of bumpers and a trunk lid for my 68 galaxie that way- mind you those bumpers and their brackets are pretty heavy- both bumpers and brackets via greyhound 108 bucks. Trunklid was 97 or 98 bucks.
The size restriction isnt bad, but cant be over 100 pounds.
http://www.shipgreyhound.com/
Biggest issue is knowing when it gets there- if you write the recipients phone number on the address label they will usually call them and let them know...