looking for a frequency generator with an accuracy of 0.01 hertz

Consider putting the counting in external chips, consider the SN74LV8154 or other parts you may have available. http://www.ti.com/lit/ds/symlink/sn74lv8154.pdf. Also consider what time base you want to use, it does not have to be one second. With external counters it can be whatever you want. If you are in a hurry you can phase lock the signal and multiply it up before counting but careful the accuracy may kill you. For more information and a design look here: https://www.nutsvolts.com/magazine/article/august2014_reedhttps://www.nutsvolts.com/magazine/article/august2014_reed
Good Luck & Have Fun!
Gil