I likely have syringomas, a subtle chicken skin-like area under the eyes with small bumps. What treatments are available? (Photo

Any method will result in a scar that replaces the syringomas.  Your skin is light and generally the scar is much more acceptable than the syrigomas.  You do not have that many so one option is to simply ignore what you have and rely on an under eye concealer. If you are going to have syringomas removed, I recommend having only one or two removed as a test to see how you do.  If it is successful and satisfactory, more can then be done.

Based on your photograph, it appears as though you have milia in your lower lids. This is best treated using a sterile needle to tease out each of the hard comedones. If in fact you have syringomata, the best treatment I've found is to excise them. The red spots will look pretty bad without makeup for awhile, but I find they heal very nicely. I've attempted CO2 laser on syringomata, but with less success.