We study the multi-wavelength properties of a set of 171 Ly \alpha emitting candidates at redshift z = 2.25 found in the COSMOS field , with the aim of understanding the underlying stellar populations in the galaxies . We especially seek to understand what the dust contents , ages and stellar masses of the galaxies are , and how they relate to similar properties of Ly \alpha emitters at other redshifts . The candidates here are shown to have different properties from those of Ly \alpha emitters found at higher redshift , by fitting the spectral energy distributions ( SEDs ) using a Monte-Carlo Markov-Chain technique and including nebular emission in the spectra . The stellar masses , and possibly the dust contents , are higher , with stellar masses in the range \log M _ { * } = 8.5 - 11.0 M _ { \odot } and A _ { V } = 0.0 - 2.5 mag . Young population ages are well constrained , but the ages of older populations are typically unconstrained . In 15 % of the galaxies only a single , young population of stars is observed . We show that the Ly \alpha fluxes of the best fit galaxies are correlated with their dust properties , with higher dust extinction in Ly \alpha faint galaxies . Testing for whether results derived from a light-weighted stack of objects correlate to those found when fitting individual objects we see that stellar masses are robust to stacking , but ages and especially dust extinctions are derived incorrectly from stacks . We conclude that the stellar properties of Ly \alpha emitters at z = 2.25 are different from those at higher redshift and that they are diverse . Ly \alpha selection appears to be tracing systematically different galaxies at different redshifts .