Hourly CO2 fluxes, generated from a biosphere model applied to the Australian region, are used to produce synthetic CO2 atmospheric concentration data. The concentration data are inverted using a Bayesian synthesis method, to test whether the CO2 fluxes can be successfully retrieved at monthly temporal resolution. The inversion is performed globally (with a base network of about 100 sites), but the tests focus on the Australian continent, subdivided into 12 regions. The inversion is tested using dense networks of approximately 40 new sites in and around Australia. Land-based and offshore networks are compared. The land-based network produces biased source estimates, for regions with large diurnal source variability, if the inversion only solves for a constant flux throughout the month. The bias is eliminated when we solve for two fluxes for each region, a constant monthly flux and a daytime-only flux. The offshore network gives large uncertainties and biases for inland regions of Australia. These latter biases are not significantly improved by solving for the daytime flux. The inversion that includes daytime fluxes is used to design a network to minimize the average annual mean uncertainty for Australian sources. Networks designed using incremental optimization are compared with some reference networks. Site locations are found to be sensitive to the data uncertainty applied to each site. The incremental optimization method appears to be most effective for networks of fewer sites than about half the number of regions being solved for.