I've been working on this project for a couple months now, and I finally had a success. The problem with using standard teleconverters on the Leica X1, aside from them usually being low-quality crap, is that they generally have a rear diameter of about 37mm causing severe vignetting.
The idea behind a teleconverter for compact cameras or camcorders is that you not only have a small lens, but you have also zoomed it to capacity, which further reduces the field of view. Therefore, a 37mm rear diameter is usually enough. Not so with the X1. I've experimented with several zoom lenses but was unsuccesful until now.
Enter the Samigon 200mm 1:3.5 AUTO-TELE lens No. 35855. I picked this one up on eBay for $15.99 including the cost of shipping. Unfortunately, I don't even know what kind of camera it was made to fit. I was only familiar with the Samigon brand because I have an old Samigon zoom for my Canon AE-1.
Unscrew the retaining ring at the top of the lens and remove the elements. It's easiest to put your finger over the end and then carefully turn it upside down on your workspace. Then unscrew the flared portion of the housing from the rest of the lens.
You'll need the three lens elements as well as the three metal pieces that fit the elements and the end retaining ring.
Life would be far too easy if the X1 was able to focus through the elements without any modification. However, it just takes a little bit of rearranging to bring the three lenses close enough together to make it work.
Start by putting the medium-sized metal ring into the bottom of the flare case like this.
Put the smallest element into the smallest metal ring, bubble side up.
Carefully place the small metal ring and lens into the casing on top of the medium-sized metal ring.
Be careful not to smear the lenses with your fingerprints.
Place the medium lens onto the small lens, bubble side up. Once again be careful not to get finger smudges all over the lenses.
Center up the lenses in the casing.
Carefully place the largest element onto the medium element, bubble side up.
Be careful not to smudge the elements and make sure they are centered up and seat on one another.
Set the remaining medium-sized metal ring on wide side down on top of the large glass element. Center it up the best you can.
Screw the retaining ring into the threads on the casing until the glass is tight in the case.
The Leica X1 and all other cameras can now focus through the three elements creating approximately a 2X zoom.
In their original positions, the metal rings created small spaces between the glass elements. They had to be relocated, so that the glass could touch but that the combination still retained the approximate height, so that it would screw together tightly in the case.
Take a test shot with your Leica X1 from a fixed location.
Now place the teleconverter over the lens of the X1 and take the same shot.
See any difference?
(Mounting and adapter construction coming soon. I'm tired tonight.)
Update: I actually shot the entire 2011 Houston Art Car Parade with the X1 and the teleconverter. You can check out the results here: http://www.flickr.com/photos/ffacker/sets/72157626658792693/