  We present a physically motivated model to estimate the molecular hydrogen
(H2) content of high-redshift (z~5.7,6.6) Lyman Alpha Emitters (LAEs) extracted
from a suite of cosmological simulations. We find that the H2 mass fraction,
(f_H2), depends on three main LAE physical properties: (a) star formation rate,
(b) dust mass, and (c) cold neutral gas mass. At z~5.7, the value of f_H2 peaks
and ranges between 0.5-0.9 for intermediate mass LAEs with stellar mass M_* ~
10^{9-10} solar mass, decreasing for both smaller and larger galaxies. However,
the largest value of the H2 mass is found in the most luminous LAEs. These
trends also hold at z\sim6.6, although, due to a lower dust content,
f_H2(z=6.6)\sim0.5 f_H2(z=5.7) when averaged over all LAEs; they arise due to
the interplay between the H2 formation/shielding controlled by dust and the
intensity of the ultraviolet (UV) Lyman-Werner photo-dissociating radiation
produced by stars. We then predict the carbon monoxide (CO) luminosities for
such LAEs and check that they are consistent with the upper limits found by
Wagg et al. (2009) for two z>6 LAEs. At z\sim(5.7, 6.6), the lowest CO
rotational transition observable for both samples with the actual capabilities
of Atacama Large Millimeter Array (ALMA) is the CO(6-5). We find that at
z\sim5.7, about 1-2% of LAEs, i.e., those with an observed Lyman Alpha
luminosity larger than 10^{43.2} erg/s would be detectable with an integration
time of 5-10 hours (S/N=5); at z\sim6.6 none of the LAEs would be detectable in
CO, even with an ALMA integration time of 10 hours. We also build the CO `flux
function', i.e., the number density of LAEs as a function of the
line-integrated CO flux, S_CO, and show that it peaks at S_CO = 0.1 mJy at
z\sim5.7, progressively shifting to lower values at higher redshifts. We end by
discussing the model uncertainties.
