Where are you at? What types of grasses do you have locally. Grass seed for cool season grasses need a soil temperature of around 60 degrees (somewhere around that or above) and above to germinate. Figure 10 days to 2 weeks to germinate with the ground being kept wet/damp the entire time. The hard ground would have to be worked. In a month in the right climate you will have some widely spaced sprouts assuming a warm climate like florida. In the cold climates which is most of the country, it is too cold and you won't get any grass to grow till spring. Best bet is to call your local nursery. Then try to buy some sod somewhere and put it in. This is the wrong time of year for fresh sod, so maybe you can find a nursery who will cut you a patch for the grave. Then you will need to cut down the old part over the grave to place the sod down with fertilizer and water.