how can one appear in other states counseling for private MBBS COURSE through neet exam, what is the procedure.

First of all be very clear that you don't need any state domicile to apply for any private medical college in India. There are many states which have their own association for private medical colleges.Most of the States have dmer sites where they list all the activities related to admissions, counseling, merit list and stuffs. I'll list some of them-

1 Comedk - Karnataka

2 Mpdmat/mpdmer- M.P

3. Upcmet/ kgmu - U.P

4. Cgdmer- Chattisgarh

5. Dmer- Maharashtra

Most of the colleges will conduct its own personal counselling specially the deemed ones so you need to keep checking those sites frequently.