Need help selecting a mosfet to vary switching regulator output
The TPS61236 datasheets mentions a suggested feedback resistor current of approx 100 x the feedback leakage current: 100 x 120nA, 12mA


WRONG! 100x 120nA is not 12mA, but 12µA!

It has a 1.2V reference, so for 12µA in the lower feedback resistor we get 100 kOhm. The datasheet uses a 330k resistor.

Anyway. Let's go with 50k to be safe.

You need a FET with RdsON less than 1% of 50k, ie, 500 ohms. 

Any MOSFET these days will have much lower RdsON, so this means basically pick the cheapest dual NMOS you can easily find. Just make sure it is specified for the gate drive voltage you will use.

A suitable package would be SO-8 or SOT223 or smaller if you want. I would use a dual MOS for convenience, but you can also use two single MOS of course.

Now, you can also use microcontroller outputs or any IO from, say, an I2C IO expander you have lying around instead of a MOSFET, provided you can tri-state them. Simply connect the output to where the drain of the FET is in your schematic.

Output tri-stated = MOSFET not conducting.
Output driven to 0 = MOSFET conducting.

I mean, you already use 2 IOs to drive the FETs, so you may as well skip the FETs and use the IOs to connect the resistors to GND directly!

Since FB voltage reference on your switcher is 1V2, the voltage on the open switch will be 1V2. So this will work with any IO whose VCC is 1V2 or higher.