First, the parameters:
We have a 9'6" ft inflatable dinghy. (Achillies LSI-290E) It does not have a rigid bottom or rigid floor panels. We went with the high-pressure air floor as a compromise. Its similar in rigidity to an inflatable stand-up paddle board. We do not have davits, although we would like to get them.
Now, the action;
When traveling on the ICW, we generally keep it deflated, rolled up, and tied down on deck on the port side of the seahood, as were pulling into a dock every other day for fuel and pumpout.
When we want it "at the ready", we keep it inflated and tied down on deck. There are two places it fits. Each have their drawbacks.
Position 1 is under the boom, with the stern tubes straddling the mast. This allows enough space (barely) to get by on the side decks, but does interfere slightly with the companionway hatch operation. It also makes operations at the mast a little clumsy.
Position 2 is on the foredeck. This frees up the sidedeck access, but completely obstructs access to the anchor locker. In order to anchor, we have to loosen the tiedowns and hoist its bow partly with the spin halyard. This is not ideal, but it works.
We have a small Forespar "Motor Mate" hoist that we use to move the outboard between the dinghy and the rail mount on the stern pulpit. Its a pretty easy operation. For the dinghy itself, we use the spin halyard on the bridle to hoist and lower it bow-up. Again, fairly easy as it weighs only 80 lbs.
In the Bahamas, we towed it everywhere, as it is your "car" for getting around once you're anchored, only hoisting it on deck the rare times we take a slip. We NEVER tow it with the outboard attached! One bad wave is all it takes to flip it. When towing, or for that matter any time its tied to the boat, we always use TWO lines to secure it. We've heard many radio calls for a lost dinghy that went "walkabout". Even got to go and rescue one. And we did have one bridle fail while under tow. Without the second safety line, who knows how long it would have been before we noticed!
While at anchor, we keep the dinghy in the water, with motor attached, and everything secured with cables and locks. This is where davits would be nice, both for security and to reduce the buildup of growth on the bottom.