  We present deep submillimeter imaging of two spectroscopically confirmed
z~6.5 Lyman-alpha emitters (LAEs) in the Subaru Deep Field. Although we reach
the nominal confusion limit at 850 micron, neither LAE is detected at 850
micron nor 450 micron, thus we conclude that the LAEs do not contain large dust
masses (<2.3e8 Msun and <5.7e8 Msun). The limit on their average L(FIR)/L(UV)
ratios (<~35) is substantially lower than seen for most submillimeter selected
galaxies at z~3, and is within the range of values exhibited by Lyman-break
galaxies. We place upper-limits on their individual star formation rates of
<~248 Msun/yr and <~613 Msun/yr, and on the cosmic star formation rate density
of the z~6.5 LAE population of <~0.05 Msun/yr/Mpc^3. In the two submm
pointings, we also serendipitously detect seven sources at 850 micron that we
estimate to lie at 1<z<5.
