Is there a way to find the lowest car rental rates within the month?

I always check Priceline and Expedia when I rent a car.

Nope, I worked for a rental agency. Most prices are “on the fly”, they are calculated in real time with fleet size and demand requirements used come up with a rental rate.
As @Cruiser said going with a pre-paid like Priceline will give you a low cost but you’ll be locked in to start date/time and return. If you’re half a day late because of weather or connections; you’ve already paid, no refund.
Also fleet size during the week means a lot of business rentals therefore reduces the available cars to rent, they jack the price for business customers.

I been editing trying to get a “perfecto-fish.”

@cheebdragon I have found really good rates with Dollar. They have a Lock & Low rate where you prepay.

Hertz & Dollar & Thrifty are one company, but it seems like I get the best deals on the Dollar site.

@Tropical_Willie Won’t certain days of the week predictably have high demand? I occasionally rent at the local airport, and it seems like Friday & Saturday are cheaper (business travelers are leaving town) and Sunday & Monday are more (business travelers arrive).

I haven’t kept detailed records, I could be mistaken, but that’s my impression.

Yup, @Call_Me_Jay Sunday and Monday are business days, when people on “expense reports” pick-up cars. I did that many times in the corporate world. Back in the eighties and early nineties they trips were set by a stay over on Saturday night (airline requirement).