You can look here:
University of Maryland Trapped Ion Quantum Information Group
Ca, Sr, Ba, Yb are most relevant. These elements have near-UV dipole transitions (blue arrows in the charts) and near-UV neutral S-P transitions (in text below each chart). Because temperature tuning is very poor for blue diodes, you have to find a diode with a free-running center wavelength within 1.0nm of the atomic transition. Note that the colors are generally barely outside the spec range for commercial diodes.
Nichia will pull "engineering" or "test" samples and wavelength select them. The special ones are sometimes sold directly (~3-5K). Others are snapped up by Toptica and re-sold for $8-$10K. This is a bargain compared to the only alternative: a second-harmonic generation (SHG) system, where you need a diode, tapered amplifier, and doubler (~$150k).
The funny thing is that any one of you could be sitting on a magic diode and never know it.