@Brenda984,
We have a rental in our Georgia home. We live in a one story house, and we converted the master bedroom of our house into a one bedroom apartment, which is the rental. We closed off the door between the apartment and our house, and soundproofed the wall by adding a second layer of 5/8" drywall on both sides of the wall, and used Green Glue noiseproofing compound between the two layers. It does an amazing job of stopping noise transmission between the two living spaces. It's not cheap, but it's DYI-able, less expensive than other options, and the soundproofing of the lower level will add value to your property. I purchased the Green Glue on Amazon and eBay.
If you want to soundproof the ceiling of the lower unit from the footsteps, furniture movements, TVs and conversations in upper unit, then I recommend that you insulate between the floor joists/ceiling rafters, then install two layers of 5/8" drywall with Green Glue sandwiched between them.
I also recommend that you close off the doorway between the two units if there is an easily accessible secondary entrance for one of the units. For our apartment, guests go up the steps to the back deck to reach the apartment door. This provides a major sense of privacy, and security, for all of us.