You are in a period for your father's birth where certificates cannot be viewed on line on the official pay to view site
www.scotlandspeople.gov.uk. The cut off to view birth certs on line, as images direct from the birth register is currently 1910, increasing one year every year - due to data protection.
From what you say, your mother might have some details on old documents. Good place to start

The key documents that you need to try and find would be his full birth cert, which hopefully your mother will have put away. Also his marriage cert will help you with his parents' information. This is an example of what a birth and marriage cert look like from the Scotlands People site:
Birth
www.scotlandspeople.gov.uk/content/images/famousscots/birthCharlesRMcIntosh1868.tifMarriage
www.scotlandspeople.gov.uk/content/images/famousscots/Marriagekeirhardie.tifAs you can see, they are very informative and should include full details on parents. For a birth cert, it should include the date and place of parents' marriage. If your paternal grandparents' weren't married when your father was born, this will be a little more of a problem for you when trying to find out about them. As JL mentioned earlier, his birth entry could be either the surname of Murray or McIntosh.
If your father's mother went on to (re)marry after you father was born, her new married name may be included in your father's wedding cert which is why this is also a useful document to view.
There is no death for your grandmother (using wildcards to pick up of Jean/Jane/Janet etc) with the surnames of McIntosh and Murray, even when you open up the death years for a wider search.
....But, let's take it a stage at a time and see what documents your mother has first that would help you further with the searches

Monica