When it comes to specific requests like this you get a programmer to write a script or app for your requirements. I've seen such requests before and yours is yet another variant on the repeating task question.
Figure about a week for your custom script or maybe an app.
Hello. I would like to create a calendar that can sync to my iPhone and iPad that allows me to add repeated tasks/events on certain business days. Say I have a task that I want repeated monthly on the 10th business day, and another task repeated quarterly on the 15th business day. I know you can repeat tasks on Calendar days. Only thing I have seen is Omnifocus, but that costs quite a bit. Anyone have any suggestions on online services that do this for less? Any way to get google calendar or anything else to do this? Thank you.