How to invert an open drain output?
Connect a pullup resistor to your existing open drain output, so that it goes high when it is not actively pulled down.

Connect the existing open drain output to the gate of a MOSFET. A 2N7000 might be a good choice. Connect the source of the MOSFET to the negative power line. The drain of the added MOSFET will be the new open drain output to the counter.

When the original open drain output pulls low (is driving low) the new MOSFET will be disabled...open drain. When the original open drain output is disabled (pulled high through the pullup resistor) the MOSFET's drain will be driven low.