Of the loads Boomer suggests, the 7 grains of Unique is by far the lightest and may only be in the 1200 fps range, with a 150, or 165 or so, cast bullet. I would experiment with this and go from there downward. That is still darn fast, as compared to a pistol, except the magnums, and a 38 special say, will tear a grouse up pretty bad. I have esperimented with "basement" loads in the 30-06, where I actually just loaded them, then shot them in my basement, but the loads were much less than this. Even so, the lightest of loads would just make an enlarged hole at 30 feet. Getting the peewee loads to hit somewhere close to your regular sighting is the main trouble.
A far better solution is just to load an accurate load with a cast bullet and shoot the grouse in the head or neck. I have shot the heads off of quite a few grouse and ptarmigan with full power 30-06 loads.