One possibility is to save your existing power bank for other projects, and get a power bank with Quick Charge 2 or QC 3. These can be tricked into delivering 9V or even 12V for some models, by using a so-called Quick Charge trigger, a cheap device that you can buy online.
You will need to fashion your own power adapter from USB to whatever power plug the router has.
And of course you need to do some tests to ensure that:
- the trigger is doing what you want it to do (namely tricking the power bank into delivering whatever voltage you want)
- the power bank is actually able to deliver the voltage you need at the current you need, without significant ripple - power banks vary in this regard
- and ultimately that the router is comfortable with the whole situation
When all this is done, you might still want/need a USB voltage meter in order to verify that you are selecting the correct voltage at start up, unless the QC trigger has integrated indicators that can reliably provide you with this information.