4 Hz Stable Frequency generator

\$\dfrac{32768}{8192} = 4\$

Crystals are available that oscillate at 32786 Hz and you can divide this frequency down by 8192 using CMOS IC 4060, which also contains an oscillator circuit. Images are taken from here. Stability will be better than you are asking for.

Standard crystal oscillator circuits have an accuracy of +/- 20ppm to 200ppm accuracy (ppm=pulses per million) depending on the crystal used. 4 Hz +/- 0.01 Hz is an accuracy of 2500ppm. So... just about any crystal oscillator circuit will give you the accuracy you need.

The problem that you'll find is that a crystal oscillator will run at much higher than 4 Hz. 32.768 KHz is about the lowest you'll find, with the upper end in the hundreds of MHz (or maybe a GHz or so). So what you'd do is use a higher clock frequency and divide it down to get the 4 Hz you desire.

Exactly how you do it all depends on what you're comfortable designing and building. You can use a metal-can type oscillator and then divide it down with simple counter chips. Or you could use a CPLD or FPGA (overkill). Or even a small microcontroller for both the crystal oscillator and the divider.

I would use the microcontroller approach. If you have never done a microcontroller approach, it is probably more difficult to do. But it's fairly flexible, low power, and small size. Although I'll be the first to admit that this approach isn't for everyone.