What does the impedance look like around a small resonant loop?
This kind of stuff is notoriously difficult to predict.  Analisys will only get you so far.  Then you have to experiment and tweak.

Basically you have a parallel L-C resonant circuit.  If this is a small loop relative to the wavelength, then you have mostly a lumped system.  That means that the current thru the whole loop is pretty much the same at any one time.  The impedance between any two feed points goes up linearly with the angle between them.  Think of the loop as a auto-transformer. Don't let the fact that it only has one turn get in the way of that.  Tapping off some section of the loop is like two taps in the auto-transformer winding.  Given that the whole winding has some fixed impedance at the desired frequency, the impedance between the tap points goes down proportional with the fraction of the winding being tapped.

I used a loop like that in a product to receive 434 MHz.  The loop was about 1 inch in diameter, and the tap points to get 50 &Omega; were about 1/4 turn apart.  I don't remember the cap value, but somewhere around a few pF.

In the prototype, I put two pads for the resonating cap in series.  That allowed easier experimental tuning of the loop to the desired resonant frequency.  I also put a whole bunch of tap points in the loop, then we tried different combinations experimentally to pick the best impedance match to the circuit.

Added:

I dug the board I mentioned above.  Here is the layout of the resonant loop antenna:



C24 and C25 in series are the resonating cap.  Being in series made it easier to tweak the overall capacitance a small amount.  The total ended up being a few pF.  R19 is only there because someone wanted to experiment with damping.  It was never used.  The two thru-hole pads to the left of the loop by C23 and C27 are the RF feed points into the circuit.  Wires were installed between them and the right holes in the loop, which were determined by experimentation.  Now that I see this again, I think the feed points were more like 45-55&deg; apart.  The diameter of the loop was .9 inches, and the RF frequency was 434 MHz.