TPS61081 - FET Recommendation for PWM dimming

There is no recommendation.  I suggest a FET with turn on speed at least 100x faster than your PWM signal.  Also, I suggest adding 10 ohm resistor in series the FET's gate to prevent any ringing/overshoot at the gate.  Also, I suggesting placing at least a 100 ohm resistor in series with the drain so that the SS pin is not pulled completely to ground.

I am sorry.  I was not clear.  In Figure 24, the circuit is switching between ILED(high) = I(ss) * R1 / Rset and ILED(low) = I(ss) * (R1||R2) / Rset.  Alternatively, you could switch between ILED(high) = VFB / Rset and ILED(low) = I(ss) * R2 / Rset, where I(ss)*R2 < VFB and R1 is not used.  If ILED(low) is supposed to be 0, then I recommend R2 be 10-100 ohm so that the SS pin is not pulled completely to ground.