Choosing a Tantalum based on Min. ESR - LDO Stability
The best way to deal with a LDO that requires a minimum ESR output cap is to use a different LDO.

These LDOs were designed when anything more than a few 100 nF was too big for ceramic or any other technology that has very little ESR.  Tantalum was the usual choice for a few &micro;F to a few 10s of &micro;F.  These had some inherent ESR, so LDOs were designed to be stable with them.

Somewhere around 2000 multi-layer ceramic caps became small, cheap, and available enough to replace tantalums in these applications.  Newer LDOs were designed with these in mind, and are stable even if the output cap has 0 ESR.  This latter arrangement is better, because the cap does it's job better the lower the ESR is.  You want the LDO plus cap to look like as a low a impedance as possible to the rest of the circuit, and having some resistance in series with the cap defeats that to some extent.

If you really really need to use one of the ancient LDOs that require a minimum ESR, you can use a ceramic cap and add a resistor in series with it.  You can try to find a tantalum cap that specifies the minimum ESR required by the LDO, but those are getting harder to find in the range ceramic can nowadays cover well.