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_sun 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.
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