NYS Vehicle & Traffic Law, Article 9. paragraph 375.20:
(g) In the event, however, that such an omnibus, equipped as herein provided, shall cease to be
used to transport pupils or pupils and teachers or children of migrant laborers and migrant child care center instructors, or children and camp instructors, the equipment, markings and paint, herein provided for, shall be removed and changed within fifteen days after relicense. Nothing contained in this section, however, shall be deemed to waive any other requirements as to equipment, markings and paint, contained in this chapter.
The list in 375.20 includes:
a. flashing front and rear lights, at least one red in each direction;
b.c.d. Black on "National School Bus Chrome" signs saying "School Bus," plus a handicapped symbol if wheelchair equipped, signs lighted between sunset & sunrise;
e. 8-inch convex mirror on a [dog nose hood],
f. signal lamps and signs in accordance with rules to be adopted by the Commissioner of Motor Vehicles
375.21 Every motor vehicle having a seating capacity of more than seven passengers, and used primarily to transport pupils or pupils and teachers to and from school, shall be painted the color known as "national school bus chrome."
In the event, however, such a motor vehicle so painted shall cease to be used to transport pupils or pupils and teachers, the color of paint herein provided for, shall be changed to another color, within fifteen days of relicense.
The Commissioners of Motor Vehicles and Transportation may make rules requiring:
21-b Two-way radios
21-c Stop arms front and rear
21-d Back-up beepers
21-e Front crossing arms
21-f Safety Sensor Devices
21-g Back-up beepers required
21-h Reflective tape required
21-h Engine fire suppression systems required on wheelchair buses.
Note: There are two sections 375.21-h in the law, it is not my typo. And 375.21-a deals with used police cars in the section about school bus equipment.
One can presume that the devices in 375.21 are also included in what must be removed per 375.20 (g).
I don't think the engine fire suppression system or the convex mirror on a dog nose are required to go, but all the other markings are a good bet to take off.
So, to register it in New York, you have no choice. The trappings of carrying school, church, or camp children have got to go.
The stories I have read here on Skoolie.net indicate that some states don't care at all about the color, and some states will let you go through in a yellow bus if it is legal in your home state, even if they would not allow it in theirs. And other states will ticket or maybe even put out of service a yellow bus even if it is legal in its home state without regards for reciprocity. But yellow and markings are not legal in your home state, so it's a moot point.