Hi Ed,
During our characterization of the TPS709xx we determined that in order to remain stable, you can have a maximum capacitance of 47uF with ESR between 0 and 0.2 ohms. We do recommend X5R- and X7R-type ceramic capacitors; however, as long as your Tantalum capacitor has ESR between 0 and 0.2 ohms over the operating conditions, a Tantalum capacitor should work.
Very Respectfully,
Ryan