How do I get Captivate 9 to work with my annual Captivate 2017 SN?

You talk about a SN, which would mean you have a perpetual license, not a subscption license. For a subscription license you don't need a SN, only the Adobe ID linked witht the subscription. If it is a subscption license, Rod gave you the answer.

When did you first purchase this subscription?  Was it during Captivate 9 or Captivate 2017?  If your first install under the subscription was for Cp 2017 I don't think you can then install Cp9.

Moving this discussion to the Getting Started forum.