We simulate deuteron production in Pb+Pb collisions at 2.76 TeV and focus particularly on the elliptic flow. In coalescence, the deuteron yield depends on the size of the region that produces the coalescing nucleons. The elliptic flow also depends on how the size of the effective emitting region varies with the azimuthal angle. Thus the elliptic flow of deuterons from coalescence is expected to be sensitive to the azimuthal anisotropy of the fireball more or at least differently than in case of statistical thermal production. We test this idea by using the blast-wave model to parametrise the emission of hadrons and also deuterons in case of thermal production. We tune the model very carefully on proton and pion data for spectra and differential elliptic flow. This procedure constrains it quite precisely. It turns out that coalescence leads to higher elliptic flow than the thermal production and is in better agreement with current data.