Epoxy would kinda do the trick but you would have to paint over it. It's not the cheapest stuff either. You would need a thickener as well, because epoxy is very runny if not thickened. You would have to clean out the rotten wood really well or it will continue to rot and your fix will fall out. Good luck.

All it will do is buy you a little time. It's a quick, cheap, temporary fix. A couple years ago I had a door frame (walk-in door to garage) that had rotted out a little at the bottom. I cleared the hole well and inserted some epoxy type material, smoothed it over, repainted and went on my merry way. Recently went to repaint the door frame and while the epoxy area was still hard, there is now an area around it about 3-4" in diameter that had rotted. I decided to replace the door frame.

The Minwax Wood Hardener is resin in solvent, and will penetrate into wood very well.

If you put enough of it on, water is not going to penetrate at that point any further (the passages in the wood are now filled with resin).

I routinely us it to treat the ends of exterior wood trim (especially anything less than 1.5 inches thick)to prevent water from wicking into the wood end grain and causing failure of the paint and wood (thus accelerating the decay of the wood).

The softest material should be removed to avoid wasting a lot of hardener (and time).

You simply paint the hardener on repeatedly, allowing it to dry between coats.
A film will eventually start to form and then you can stop.

The drying time increases as less of the hardener wicks into the wood and more stays on the surface.

At this point you can use the Minwax high performance wood filler to replace any missing material.

The filler can be carved and shaped when partially hard very easily.

Once it fully hardens it is a little more work to carve, but not really any worse than wood.

You can even texture the filler to match the surrounding surface.

Some primer and paint and you are done.

If you have stained wood there is no good way to repair it if it is outdoors without actually replacing the damaged wood with more wood (and even that will usually show).

It is not like furniture repair that you can use all sorts of tricks to make a patch blend.

Outdoor exposure is much harsher on the finishes, and will then mess up the repair.

Thank you all for your comments and time. I went ahead and purchased the minwax and we'll see how it goes. That's a great point brick about doing the ends. This gives me all sorts of ideas for other projects.

The ends of rafters get a good soaking before the fascia goes up, along witht eh ends of any fascia pieces.

A friend had corner boards made from 1x lumber rot at every joint in less that 3 years .

After making the longest pieces we could we saturated the ends of every piece for a few hours in a large can if Minwax hardener.

The paint is still good and the boards are fine ten years later.

Some of the corner boards (outside corners) on the back of the house are 3 stories high.