Build a small box with a piece of an unused HEPA filter for a vacuum cleaner, sandwiched between two small computer case fans in push/pull config, add some batteries and a on/off switch. Take that on the train and leave it whirring. Store it in a ziploc bag that you open after getting on the train and close before leaving again.

You then have to send that sample off to a lab, since DYI-ing an elementary carbon analysis looks bloody complicated and expensive.