We present deep submillimeter imaging of two spectroscopically confirmed z \sim 6.5 Lyman- \alpha emitters ( LAEs ) in the Subaru Deep Field . Although we reach the nominal confusion limit at 850µm , neither LAE is detected at 850µm nor 450µm , thus we conclude that the LAEs do not contain large dust masses ( < 2.3 \times 10 ^ { 8 } M _ { \odot } and < 5.7 \times 10 ^ { 8 } M _ { \odot } ) . The limit on their average L _ { \mathrm { FIR } } /L _ { \mathrm { UV } } ratios ( \lesssim 35 ) is substantially lower than seen for most submillimeter selected galaxies at z \sim 3 , and is within the range of values exhibited by Lyman-break galaxies . We place upper-limits on their individual star formation rates of \lesssim 248 M _ { \odot } yr ^ { -1 } and \lesssim 613 M _ { \odot } yr ^ { -1 } , and on the cosmic star formation rate density of the z \sim 6.5 LAE population of \lesssim 5.0 \times 10 ^ { -2 } M _ { \odot } yr ^ { -1 } Mpc ^ { -3 } . In the two submm pointings , we also serendipitously detect seven sources at 850 \mu m that we estimate to lie at 1 < z < 5 .