Solution
Currently, there is no built-in ability to use Specialty mode in an NI 9144 or NI 9145 EtherCAT chassis.
The functionality desired by using a module in Specialty mode in an EtherCAT chassis can still be implemented, but should be done so through the FPGA.
To get started, see
Do More with LabVIEW FPGA & C Series Digital Modules using CompactRIO. This link will show how to the basics of configuring FPGA code to setup a PWM or Frequency measurement that should give you similar functionality to the specialty modes configuration.
Specialty mode can be used innately on non-EtherCAT cRIO chassis. See
Specialty Digital Configuration and
C Series Module Support for Specialty Digital Functions in Scan Mode to get started.