Running 9v battery in parallel with Power Supply
While this is not the answer to your explicit question, I must address the larger question: how can I minimize noise in my circuit? Yours is a good example of an xy problem. You need to do x, you've settled on y as a solution, and want help in doing y. What you really need is to address x.

And the most basic answer I can give is: get somebody who knows how to design amplifiers (or whatever your circuit does) have a go at fixing yours. There is simply no good reason nowadays for power supply ripple to show up in an output.

As an alternative answer: Get somebody who knows something about power supplies provide you with a new 9-volt power supply. One with negligeable ripple. Trust me, it's not hard to do.