Grumps wrote...
For a 2:1 range in resonant tuned frequency you'd need
a 4:1 range in variable inductance. That's more than
most adjustable pot-core inductors, etc., provide. A
quick review of various parts shows about 2:1 maximum.
There are several ways to create variable inductors.
One is to make an air coil and adjust a tuning slug in
and out of the coil. This may be your best approach.
Coilcraft has a nice selection of coils with tuning
slugs, but most, like the Unicoil 10mm series, can't do
a 4:1 range.
http://www.coilcraft.com/uni10.cfm
A second way is the classic variometer. Here the coil
is split into two parts, wired in series, where one of
the coils is capable of rotating within the other. If
they are aligned the inductance is nearly doubled over
a single coil. But, if the orientation of one coil is
rotated with respect to the other the inductance will
be reduced, and if they're reversed it can be very low.
http://www.qsl.net/in3otd/variodes.html
http://www.g0mrf.freeserve.co.uk/variometer.htm
http://www.crystalradio.net/crystalsets/hassell
http://www.schmarder.com/radios/misc-stuff/variometer.htm
http://www.qsl.net/in3otd/vario1w.jpg
If the coils are wound in spherical shapes, it's easier
to nest one inside the other and orient it as desired.
http://www.rubylane.com/ni/shops/wavesradios/iteml/tel002#pic1
http://www2.propichosting.com/Images/450002496/17.jpg
It's easy to get > 10:1 ratios by this technique.
You can also slide one coil in and out of the other.
http://www.radioblvd.com/DoddPix/lscplr.jpg
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=9726250166
A third method for obtaining wide variable inductance is
with a rolling slider bar making a variable winding tap.
http://www.fairradio.com/t301.jpg
The links and pictures I have provided are for working
at low frequencies with large inductors, but I imagine
most of the concepts can be miniaturized.
An interesting pot-core tuning technique that may be
useful for you is to run a DC current through the coil
to saturate the core, dropping its permeability. This
scheme could probably be used to exceed a 4:1 ratio.
An issue to evaluate is your required tuning stability.