I've put single burner propane stoves into a couple of small RV's and one boat. In these galleys the advantage to one burner is that suddenly I have counter space where there was none before (with a two-burner). I use a silicone trivet instead of a second burner as a place to, say, set a hot pot of rice while I then cook the stir fry. Works for me when the alternative is no counter space.
So here are some of the stoves I have considered or tried:
[Note: I can't figure out how to "place" images within th etext or even in any certain order at the bottom. The black one is #1, the stainless is #2, and the one with a stainless lid is one version of #3 (the other version has a cutting board instead of the lid)]
1) Seaward Princess 12-73-1000
This is a nice, black glass single burner, official marine stove with the expected safety features; however it's not made anymore so only used ones and you'd have to hunt one down.
2) Smev (not sure model number, but it's one burner with an X-shaped grate).
This is not quite an official marine stove, I don't think, but it does have a thermocouple, I believe (you have to push down and hold knob to start and if you let go too soon the flame doesn't stay on). A friend bought this for his small RV trailer and I helped install it. It's nice looking, stainless, and has grates that accomodate small pans (some don't). I just asked him for a review (he's been using it for six months now) and he said he likes it. It simmers well (low flame) and is easy to clean.
One negative is the propane hookup is a compression fitting. You can get an adapter fitting to make it the typical 3/8" male flare, but then that fitting is hooked on via the compression fitting. A minor gripe is that the "guts" on the bottom side hang down a ways and are completely unprotected. It can be dealt with but seems a bit primitive. OTOH, the stove looks nice from the top.
3) Princess "drop in" butane one burner (with flip down metal cover or wooden cutting board cover).
This is a different beast in that it is a "built in" stove but runs off the 8 oz. butane canisters (the ones that look like cans of spray paint). It sits flush with the counter top. I have one of these and no complaints on the function but a "real" propane system would always be my choice on any boat that could possibly support one. I keep the canisters in an overboard vented sealed locker, but still there is some risk associated with the seals and they are expensive for what you get, plus you have to find them and there is the waste of spent canisters. This is basically the same as the portable butane stoves you see everywhere but built in, with one exception: it has a flame out thermocouple. (The Princess brand portable also has a flame out thermocouple; whereas most portables I have seen do not. I thus carry one of the Princess portables as a spare, a possible second burner, or as a way to cook ashore.)
4) There is a Smev-like one now with a brand name something like CAN, but I have not tried one of those.