If the concrete is not an option. Learn how to repair drywall. Seriously.
Have the safe in place where you want it, drill the holes through the carpet and subfloor. (The whole carpet unraveling thing is a myth in my opinion. I've drilled many holes through carpet and never had it happen. Just use a sharp bit and the highest rpms possible.) Now go downstairs, cut a hole in the ceiling ~ 10" square. It might have to be two holes if the mounting holes you drilled are on opposite sides of the joists. Make a not of how far the holes are from the joists.
Now go to a local welding shop and buy one piece of 1/2" steel ~9" square for each mounting bolt. Have the shop blow some holes in the plate with a cutting torch (this will save you a headache and several drill bits). Make sure the hole in each plate is slightly less from the edge than the bolt holes are from the joists.
On your way home go by the Hardware store and get the correct size bolts, nuts, and washers. (Hint: If the holes in the safe are square, buy carraige bolts. This will make it a one person job. If round buy Grade 8 Hex Head bolts and get your spouse or a friend to help.)
Drop the bolts through the holes from up top. From downstairs put the steel plate, washer, and nut on the bolt. Tighten as much as possible.
Doing it this way will increase the surface area that the bolt is holding to. It will actually be stronger than if you lagged the safe to the joists. (A 1/2"x4" Lag bolt has just over 5 square inches of bearing surface on the threads. Each plate would have 81 square inches of bearing surface. If you figured 4, 1 at each corner, you'll have 324 sq. in. as compared to 20 sq.in. So over 16 times the bearing surface with the plates.)
Now all you have to do is patch the drywall below. Really a fairly easy job for a somewhat handy person. If the ceiling is textured, it does increase the difficulty some. The only problem would be when you (if ever) decide to move it. You'll have to recut the wholes and repair the ceiling again.
Wyman