Well Yeah that's electronics 101... But the only way to have a "Slow" power supply is to design one that way, by using 1. Low current linear regulators (I've used 2200uF on the output side of a 7805 and the BOD working on the processor, Very successfully). 2. By adding large (>10 ohm series "Filter" R's in the Vcc line, while a common method for isolating low power loads, should never be used for the main Vcc unless the load can tolerate being powered up "later". and 3. using a primary power source that can't fully supply the required load current. In the past I've successfully used 470uF caps with 100 mA regulators both 78L05's as well as LM2931's to power PIC processors in low speed low power applications with great success with the BOD enabled. The Basic Layout I used was a 100 to 470uF electrolytic right where the battery connected to the PCB. This part isn't so much filtering or 'decoupling' as it is compensation for a low battery charge condition, because the batteries internal resistance increases when the battery is nearly discharged and the addition of this part enables the use of a little more of the power in the battery. After the linear regulator I would use between 47 to 220 uF (depending on what the board had to do) a 10 to 22uF tant cap somewhere in the "middle" of things and a 100nF cap for each IC right at the IC. What works in one application usually won't work in production and skimping on bypassing because you don't fully understand the topic is usually a waste of time because the circuit might work well in the test configuration usually doesn't when everything is interconnected. You will have greater success if you remember that...
Murphy was an optimist..
Bob