TPS62090 output ripple and phase margin

It's just a buck converter, so the output voltage ripple can be reduced by increasing the inductance and/or output capacitance.

You can measure gain and phase with this app note: http://www.ti.com/lit/an/slva465a/slva465a.pdf  If you use any of the LC combinations in the datasheet, the circuit will be stable.

Please remember to add some more words to your post title, describing what it is about.

Customer  Need to know the Gain Margin and the Phase Margin for the Webench [it's very important]:

 Vin=3V-5.5V

Vout=1.2V/3A

1. with Co =22UF

2. with Co =47UF

Can you help?

We do not have yet the EVM.

Can someone test it  for us?

We do not have the resources to do specific testing for every customer.  I can assure you that your design, assuming your inductor value is in the recommended range, will be stable with either 22uF or 47uF output caps.  These are both in the datasheet as recommended LC combinations and are thus stable.