You might struggle to get a container on one, even if there was space left....
https://www.youtube.com/watch?v=iwbPdF5dIgQ
"There is a small number of suburban "liner" trains on the JR network, e.g. Home Liner, which require a special "liner ticket" and are not covered by the Japan Rail Pass. However, since these trains are targeted at suburban commuters, foreign tourists are unlikely to use them. Confusingly, there are also a few trains that contain "Liner" in their names, but do not require a liner ticket, such as the Marine Liner, Seaside Liner and Ishikari Liner. These trains are fully covered by the Japan Rail Pass."
http://www.japan-guide.com/e/e2361.html