I know that the key component is a variable capacitor if my memory
serves me.

Actually, if you're only interested in using the loop to manipulate signals on
one frequency (the one shared by the two stations your radio is 'fightin'
over), you could wind the loop to match that frequency only, and omit the
variable cap altogether.
That being said though, as long as you're going to build a loop of some sort,
you might as well build it to help you on all the MW frequencies, and those
'elusive' tuning caps aren't all that elusive or expensive when you consider
what they can do for you. The Xtal Set Society (I believe
www.midnightscience.com, but do a search for Xtal Set Society) has 10-365pf
variable caps for around $10 before shipping. So does Ocean State Electronics
(again, not having the URL handy, just do a search, should come right up)... or
just search for variable capacitor and see what you find.
I have built many loops over the years, and with the exception of a few
quick-n-dirty experiments made from REALLY cheap materials, they all worked
quite well at nulling between stations and fighting noise. The very first loop
I built was about 7 years ago, and worked very well, even for a novice
builder/user. 10 windings of #20 wire on a crossbar frame, tuning cap from an
older (VERY scorched and dead) radio, and plugged right into my radio. Put the
whole thing on a lazy susan turntable and you're working MW in style!
Best of luck-
Linus