We have measured the production of light nuclei (A<~3) in 11.6 GeV/c Au-Au collisions at the Brookhaven Alternating Gradient Synchrotron (AGS). The transverse mass spectra are analyzed using a thermal fireball model, and the yields for different particle species are discussed assuming coalescence and fragmentation as possible production mechanisms. The wide acceptance range of the 3He measurements permits a broad study of the coalescence parameter B3 as functions of transverse momentum and rapidity. Comparisons with data obtained previously at AGS energies suggest that the simple models are insufficient to describe fully the production mechanisms of light nuclei.