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From: Railroad Special Agents:

"All of the major Class I railroads and most regional carriers employ their own police departments whose officers carry the title Special Agent. Railroad Special Agents are commissioned by the Governor or other agency of the state they are employed in, are armed, and carry state arrest powers in all states in which their employing railroad owns property, if authorized by the state. Their primary concern is policing crimes against the railroad, although they sometimes have the authority to police the general public, make arrests on public property, and enforce applicable local, state, and/or federal laws when necessary."
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Thus as sworn, full-time law enforcement who are armed and have arrest power, "railroad police" would be authorized to carry firearms onboard an aircraft if they had a letter from their department stating a need for them to have their weapon accessible from the time they would otherwise check the weapon until the time they would retrieve the weapon after deplaning.