We have investigated the low-lying states of Co59 by means of the (He3, d) reaction on Fe58, using an incident beam whose energy was 22 MeV. In addition to strong l=3 transitions to the 72- ground state and a group of states centered at 2.08 MeV, strong l=1 transitions to the first, third, and fourth excited states were observed. From these results and the results of previous experiments, the first and third excited states can each be assigned spin and parity of 32-. These assignments are consistent with the results from our study of the Ni60(d, He3) Co59 reaction. The present results are in agreement with previous assignments of either 1/2 - or 32- for the fourth excited state, but cannot distinguish between these values. Spectroscopic factors for these transitions were obtained from a comparison of the experimental data with the predictions of a distorted-wave calculation.