Greg,
This cannot be easily resolved, I don't believe.
Here is how to set about figuring out the solution: Build a timing diagram. This will show you, visibly, what signals you have, what you need, and probably, how to get them. Include logic, as applicable.
This can be resolved in a number of ways, and I can help you decide which one. First, if the application is slow, you can use software. If it is fast, you can use software/hardware to a point. If it is very high speed, you will need to resolve it with hardware.
Software: Use your timing diagram to trigger on the signals. YOU are the source of the signal out/trigger, so you can setup the trigger in software.
Software/Hardware: Use your imagination. See Hardware solution for more
info.
Hardware: This is tricky, and may involve some external hardware. Setup a counter to count your analog output (you will likely have to use a transistor or other circuit to resolve the sine wave to a pulse train.) Then, setup a counter on the MIO to output a pulse on the fifth DI. Then, set it up to output your DO 'trigger' and route that signal to the input trigger for your analog input. This will involve some creativity on your part, some serious concentration on signal routing, and a lot of patience.
I have done similar setups, so if you get into a bind, and have lots money to spend, give me a call...or just post here and I will try to help. I will NOT solve the problem for you though. I get paid to do that.
Good luck