Most grass seed needs to be buried only 1/8 to 1/4" deep, with some types up to 1/2" deep. This is pretty shallow and will require precision. On bare dirt, I think it could be done reasonably using gage wheels. BUT - are you trying to overseed into sparse grass? That may be more difficult.
I don't think the aerator will be a good starting point. I think you could do something using tiny chisel points or small discs to open a furrow in the 1/4" deep range and then have a little chute to put seed in, and a press wheel to close the furrow. A cultipacker can work as the press wheel. It will take some work to build. You might want to look at either professional seed drills for grass or at gardener type seed drills for garden quantities of row crops to get some ideas.
If you like this as a design and build challenge - great! If you just want your lawn seeded, forget it. Instead, harrow the lawn with a chain or tine harrow, broadcast seed (with a push spreader, 3pt spreader, or by hand) then harrow again or use a cultipacker, water and you should be done. Don't do anything too aggressive after broadcasting seed, it's easy to bury the seed too deep for it to grow well or at all.
Another alternative to just get the job done - level the lawn with whatever implement you want or already own, broadcast seed on the surface, then spread straw or another mulch that grass seedlings can grow through, and water. This is what a lot of pros do for lawns. It works pretty well, actually, as long as the soil is not compacted solid. (Unfortunately it is often used around new tract homes where building codes require soil to be compacted thoroughly, which is good for stability in the short term but terrible for getting grass to grow.)