Is it possible, yes. Certainly depends on the dinghy. Something like the "Sport Yak 213" only weighs 46# and is 7' long x 3'9" wide. We used to say that they were indestructible and so ugly no one would steal one! They are practical hard boats.
If you want something larger, then you could build a rack which extended over the cockpit. I have seen this on some 22's. You can incorporate a sun shade instead of a Bimini. (Or the cantilevered Bimini if you have some extra cash).
Larger boats will probably weigh more. One brat back a few years ago, had a system to put a Portland Pudgy on top of the cabin of a 22. I would go for a davit, but that may be pushing it on a 19...
We prefer an inflatable (since 1962) as our primary dinghy because of the soft sides and not having to worry about scratching the gel coat. Also the hard dinghy has much more load capacity for the size. We have had several hard dinghies as a second boat on our larger vessels. Those we put fire hose filled with foam around the gunnel to act as a fender.
We carried our Fatty Knees 9' sailing dinghy on the foredeck one season in AK on the Cal 46.--Rarely used it, and had a RIB on the aft deck. Hoisting the hard dinghy aboard even with an electric winch was just too much of a hassle. Next season we went with a smaller second inflatable.
