Is it correct to say "This train not taking passengers"?

Solution 1:

It's fine for train-station announcements and the like. A form of ellipsis. Means dropping some syntax. Got it?

ellipsis |iˈlipsis| noun ( pl. -ses |-sēz|) the omission from speech or writing of a word or words that are superfluous or able to be understood from contextual [NOAD]

Just don't use this particular form of ellipsis in formal writing and you should be fine.