Are there ways to increase my Season Pass rank besides challenges?

You can rank up instantly by using Gems.
Please see the following page for instructions on how to obtain Gems:

• How can I purchase Gems?

To increase your rank by spending Gems, follow these steps:

1. Tap Season Pass on the home screen.
2. Tap the Gems icon displayed near your current rank.
3. A confirmation screen will appear. Tap Advance.
   * If you do not have any Gems, the purchase screen will appear.

Note: The number of Gems required to rank up varies depending on the rank.
When you rank up using Gems, you will start at 0 points for the next rank, regardless of the points remaining until you reach the next rank prior to using Gems.