The ILC damping rings will need a large acceptance to ensure good injection efficiency for the high-emittance, high-power beam from the positron source. The damping rings also need to have very low natural emittance for the collider to reach good luminosity. Meeting the simultaneous requirements for large dynamic aperture and low natural emittance presents a challenge for the lattice design. Previous designs have been based on theoretical minimumum emittance cells in the arcs; here, we present two lattice designs using simple FODO cells. The first design is for a 5 GeV ring with 16 km circumference and a layout similar to the TESLA "dogbone" damping ring. The second design is based on the same optics, but the circumference is reduced to 6.3 km by eliminating part of the long straight sections; this results in a small improvement in the dynamic aperture. The shorter ring also operates at the lower energy of 3.74 GeV. A drawback with both designs is that the high dispersion in the arcs leads to a large momentum compaction, which in turn leads to a requirement for a very high RF voltage, and a large value for the synchrotron tune. As well as presenting the designs and an analysis of the dynamic aperture in each lattice, we briefly consider the collective effects and, for the 16 km lattice, discuss the coupling bumps needed to reduce the space-charge tune shift.