We have studied the magnetism of Ag-coated Fe islands on W(110) by nuclear resonant scattering of synchrotron radiation at the 14.4 keV resonance of (57)Fe. Separated islands with an average diameter of 2.0 nm and monolayer thickness are formed at a Fe coverage of theta = 0.57 bulk monolayers. Time spectra of the nuclear decay were measured in the temperature range from 4.5 to 300 K. We find strong evidence for perpendicular spin orientation, which most likely results from the interplay of shape anisotropy and elastic strain in the islands.