We present Spectral and Photometric Imaging Receiver (SPIRE) spectroscopy for nine early-type galaxies (ETGs) representing the most CO-rich and far-infrared (FIR) bright galaxies of the volume-limited Atlas3D sample. Our data include detections of mid- to high-J CO transitions (J = 4-3 to J = 13-12) and the [C I] (1-0) and (2-1) emission lines. CO spectral line energy distributions (SLEDs) for our ETGs indicate low gas excitation, barring NGC 1266. We use the [C I] emission lines to determine the excitation temperature of the neutral gas, as well as estimate the mass of molecular hydrogen. The masses agree well with masses derived from CO, making this technique very promising for high-redshift galaxies. We do not find a trend between the [N II] 205 flux and the infrared luminosity, but we do find that the [N II] 205/CO(6-5) line ratio is correlated with the 60/100 µm Infrared Astronomical Satellite colors. Thus the [N II] 205/CO(6-5) ratio can be used to infer a dust temperature and hence the intensity of the interstellar radiation field. Photodissociation region models show that use of [C I] and CO lines in addition to the typical [C II], [O I], and FIR fluxes drive the model solutions to higher densities and lower values of G0. In short, the SPIRE lines indicate that the atomic and molecular gas in the CO-rich ETGs have similar properties to other galaxies. As might be expected from their low levels of star formation activity, the ETGs have rather low excitation CO SLEDs, low temperatures inferred from the [C I] lines, and modestly lower [C I]/CO ratios.