As far as I know all requests for unrestricted CoS allocations must be made online through the SMS by someone who has access to the SMS, there is no paper form. You need to find out why the previous request was rejected and address the issue.
The online process is described in Guide 7, p38 onwards:
https://www.gov.uk/government/uploads/s ... icence.pdf
Suggest you phone the UKVI employer helpline 0300 123 4699.
Processing allocation requests usually takes around 1-2 weeks and the migrant's leave only expires in 2 months time, that is why a request for urgent treatment is unlikely to be entertained.