Is there a good way to fill a pocket hole in a finished piece of wood?
There are many ways to fill the holes.  Here's a good link that shows a comparison of what the results look like for six different methods: http://fixthisbuildthat.com/6-ways-to-plug-fill-pocket-holes-how-to/.

Getting the appearance to match in a visible area is the problem.  You can under-fill the hole with any type of filler and then fill the last bit with glue and sawdust from the same wood.  You can experiment with stain to match the color, but the grain pattern won't match.

You can do better with wood plugs.  Kreg sells plugs of various woods, although you can probably find pine ones at your local hardware store.  If you can get plugs in the same wood, you can stain it in advance to match, then glue it in place.

If you can't find plugs in matching wood, and the available woods stain noticeably different, you can use a plug cutter to cut you own plugs from the same wood stock.  The first link above shows how to do it with dowels and a flush cut saw.  

You can use the same procedure for plugs you drill out yourself).  You may want to drill a pocket hole in some scrap to use as a jig.  Hold the plug in the pocket hole by temporary means to cut it flat.  Then you will have better access to remove it for trial staining.  

Another approach is to drill the plug cutter at the same angle as the pocket. This will produce plugs with the same exposed grain on an already flat face.  You might need to make the plugs a little oversized so you can clean up any rough edges.