A voluntary scheme was made compulsory by the Home Office last year so authorities could share caring responsibilities.
17 asked to be exempted while another 12 argued they already had "high numbers" of young people.
Croydon Council announced last year that it was unable to accept any more unaccompanied migrants children.
The Home Office has a registration site at Lunar House in the town centre.
But Croydon claimed the Government had failed to refund it in full for the costs of hosting youngsters who arrive in the town.
More than 5,000 have arrived in the last decade.
We’re waiting to hear if Croydon is one of the 29 councils directed to take in unaccompanied migrant children.