In calmer
anchorages, it is common to haul the dinghy on the davits so that it is just clear of the water. This has the added benefit of allowing you to pull the
plug if it is raining.
Another method that I have used a lot for boats without davits is to "hip" the dinghy. This involves hauling the dinghy up the side of the
hull using either dedicated dinghy falls or a
halyard. As the dinghy comes up the side, you pull up the fenders with it to prevent scratches. Once the dinghy rail is just below the rail of your
boat, you tie off the bow and stern line nice and tight to keep it from moving around.
Another method that I have seen used is making a
spinnaker pole into a boat boom. This means putting the pole out horizontally from the side of the boat with an
outhaul on it to pull a dinghy to the end of it. Your spinnaker pole needs to stick out further than your dinghy is long. To me, this seems like a lot of
rigging although using dedicated boat booms that are present on many larger vessels is quite easy.
The bungee cord sound like a good idea in your situation.