Solution
It is important to have the interface version of the NI-6509. The PCIe version differs from the others (the front end of PXIe and PCI is almost the same). This is also noted in the PCI/PXI/PCIe-6509 User Guide.
If we are speaking about the PCIe-6509 then Figure 5 from the User Guide reveals more information about the internal structure of the DIO. We have a weak (high resistance) pull-down and a user-controlled strong (low resistance) pull-up. When the pull-up is off, we have a weak pull-down DIO pin configuration. The pull-down is always there, you can't disable it.

However, since it is a weak pull-down you can build your circuitry outside of PCIe-6509. You can have the 47 kΩ in mind, and calculate voltage divider values. Here you should keep the pull-up disabled.
The PCI and PXI versions don't have any pull-up/down resistors, and you can still go with the voltage divider.