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Is there a minimum required load capacitance for the TPS22990?
Section 10.1.2 suggests that a 10:1 CIN:CL ratio should be maintained to ensure minimal dip on the VIN rail. Does this apply if we are controlling the rise-time with a large value of CT (say 10,000pF)?
There is not a minimum required load capacitance- it's whatever is needed to properly support your load. The 10:1 ratio is stated primarily to protect the supply. If your supply can handle the amount of inrush current your load will draw without the voltage dipping then there is no need to follow the 10:1 ratio. That means you can lower the peak inrush current to the point where your supply can handle it by changing dv/dt (CT pin capacitance).
