I'm afraid you're correct, your 6024E device will *NOT* support any kind of hardware-clocked digital output.
The E-series design is more than 20 years old It's probably time to move up to the PCIe bus and an X-series device (the 63xx series.)
[Edit: P.S. It *is* at least conceivable that you might be able to accomplish what you need to do using an AO task rather than a DO task. I don't think E-series supports retriggering for AO tasks natively, but there's a workaround with its counters. Unfortunately, the links I found seem to be dead at the moment, possibly a casualty of the very recent site redesign?]