I agree with vpatkhag comments. Submit HIGH school certificate ( must be having either parents name included) as a proof of DOB. Explain in cover letter that you do not ave birth certificate and you are providing secondary school certificate as a proof of DOB. This is what i did in my case.
Acceptable document for CIC is : Secondary school certificate having either of the parents name included as per the CIC returned letter. Place of birth is not mandatory and i have one case where birth certificate and passport place of birth was different ( bangalore vs mangalore), which went un noticed and guy is PR now...So better avoid this confusion and explain in cover letter that you have no birth certificate and hence providing school certificate as a proof. This will work without any issues.