Is there some software I can use to wake my iMac (10.9.5) up from sleep when I make an AFP request from another computer?
The Wake on Network access functionality doesn't work for AFP file sharing access, for some reason.
If you're not adverse to adding an extra step, you may consider using a wake-on-lan program. I'm assuming you are accessing from a Mac, as you are using AFP, so the following recommendations will be for OS X.
If you're comfortable with the terminal, I've had a good experience with wolcmd.
A GUI option that works as well (and has the added benefit of discovering the appropriate information) that I have used is wakeonlan, by ReadPixel - it says it runs on 10.3-10.5, but I can confirm it is still working on OS X Yosemite 10.10.5.
Ensure that "Wake for Network Access" is enabled in the preferences for the target Mac.