Hi Jean, Here's what I have done. It takes a little time and creativity, but you CAN make it invisible.
The first thing I would do is fill the hole. If possible, find a dowel the diameter of the hole and cut off a small piece and glue it in. Leave it just slightly below the surface of the door so there will be a little room for wood filler.
Go to Home Depot and get some wood putty. Now, I have been using Borden's colored putty one a couple of projects and have had great success with it. It comes in a small plastic tube. I have also used Minwax wood fillers for years and LOVE them., It's your choice.
Next, apply the putty to the door, being sure to leave a LITTLE more than you need so you can lightly sand it down to the same level as the wood grain. Use, I would say a 220 grit paper and a sanding block.
Now, if it's painted, it's all downhill from here.... After you get it filled, dry and sanded, take something small and slightly pointed. GENTLY follow the grain lines in the door for depth and direction. If you fug it up, you can just fill it and start over. After you put the little marks in it (I use small dental tools) rub it just a little with something like a bit of cheese cloth or terry cloth to burnish the pattern you have put in. It doesn't take much. You're trying to match the grain on the door by following the lines from point A - over the patch you have just made - to point B.
If the door is stained, you can ABSOLUTELY hide the holes and marks but it takes a little artistic talent.
After you get it filled and sanded, you will likely not have to make the marks in it but you will have to match the base color of the door as closely as you can with a stain color. Next, you will need a stain color that is the color of the wood grain. You can mix stains to achieve the colors you need. To test your colors, put a dab on a part of the door that has finish on it. be sure to wipe it off quickly with a rag dipped in paint thinner.
Ok, so after you get the base color on and well matched. let it dry at least
24 hours or longer until it is no longer sticky to the touch. Get a very fine soft bristled brush and use the darker stain to recreate the grain lines in the wood.
It takes a good eye, a steady hand and allot of patience but if you're willing to go through all of that you can save yourself a lot of denero by not having to replace the doors.
Best of luck to you and PLEASE, let us know how it goes!
One other thought, and this may be a good solution... How about just switching the hinges around on the doors? It would be easier to hide the hinge holes than the knob holes.
Kate