Thanks for the quick reply.
Right now I'm currently hitting myself for not seeing the obvious answer of using a variable resistor instead. I understand sort of how it would work in theory, I just can't seem to grasp how to put it in properly. Would you connect the variable resistor and capacitor in series with the positive terminal of the opamp, then connect the output to a resistor and the LEDs?
I would post my circuit, but it is currently in shambles, since I'm still in the planning stages. And I am looking on the internet for something that is comparable to what I want to do, but I am yet to find anything.