Hi Helge, thanks for your question!
I've not done this except next to a fire on a skewer, and it's easy to lose the fish that way. Technique helps. Pacific Northwest Indians stake filleted salmon next to an open fire, held flat with a cedar framework. Its a lot of work without a ready supply of cedar strips, but the results are wonderful (it's not a speedy cooking method). I've seen stovetop smokers for the home that are covered baking pans with a perforated divider. The meal rests on the divider and wood chips go underneath, and the whole thing goes over the stove burner. They work well, but you really can't use the pan for anything else, since it gets very smokey inside.
How about a section of stainless steel screen ("hardware cloth")? You could support it between a couple of rocks and place hot coals underneath. This is a pretty common camp cooking technique, and a lot more controllable than cooking directly over the fire. Depending on the size of the fish, you might cook the fish with skin on, wrapped in leaves, filleted, etc.
(I never catch enough fist to worry about this too much :-)