The LIRR does not have anymore dedicated "Parlour Cars" of they type I remember from my youth (you could always tell them as they had an orange or red stripe instead of blue on the side). Now they just use bar wagons of the type they have on the platforms at NYP and Jamacia. I think this is even true of the Cannonball to the Hamptons on Fridays during the summer.
While I'm not sure how they go about serving drinks and stuff, I do know that the LIRR still does offer Parlor Cars or as they call it the Hamptons Reserve Service. It is only offered during the summer months, and only to the Hamptons. It costs 17.50 more than the normal train fare to the Hamptons to ride in these cars. Coming west on Monday's it's only an extra 12.25 to ride.
According to the timetable the Parlor cars still have a red stripe, whereas the normal cars run with a blue stripe. One must make reservations and receive a special ticket to ride in the Parlor car.
I actually have been thinking of trying out this service come the summer.