Here is a sample letter that could be faxed to the Registrar to request that your marriage certificate should be expedited once you've completed the request for the certificate online. The entire process, including the next steps for expediting your marriage certificate is explained here::
The Office of the Registrar General
P.O. Box 4600, 3rd Floor
189 Red River Road
Thunder Bay, Ontario - P7B 6L8
Attention: Marriage Office
This is a letter to request your office to please process my marriage certificate at your earliest convenience. I have already ordered a marriage certificate online (Tracking #xxxxxx) . My spouse, xxxxxxx xxxxxxx, and I, xxx xxxxx xxxxx, were married on d/m/yr. I understand that this was a recent event, however, I would still like to request you to please take this letter into account when you receive my paperwork from the Officiant (licence # Gxxxxxx).
As a proof of urgency, I'm attaching a copy of xxx. According to the Canadian immigration rules, we need to apply for an extension and begin our immigration process by xxx xx 20xx. Therefore, it is absolutely essential for us that we receive the requested documents as early as possible as we are required by the CIC immigration documents checklist to attach copies of our marriage certificate and registration.
If you have any questions regarding this request, please feel free to contact me or my spouse at the information given at the end of this letter.
Thank you, once again, for your cooperation and consideration.
xxx x xxxxx
xxx xxxxx: xxx.xxx.xxxx, xxxxxx @ xxxxx
xxx xxxxx: xxx.xxx.xxxx, xxxxx @ xxxxxx
ADD FOOTER ON BOTH THE PAGES:
Ref: Marriage License# E xxxxxxx
Marriage Certificate Tracking# xxxxxxxx - x
Attachment: Proof of Urgency - Visa Stamp