After spending more time looking around, I found a solution!
I ended up using the contour option of specifying the contour line levels. I did some quick algebra to determine the minimum and maximum pressure coefficients that would result at theta = 0 and 180 deg (stagnation -> minimum -> C_p = -3) and at theta = 90 and 270 deg (C_p = 1). From here I used:
v = [-3.0:0.01:1.0];
contour(X, Y, C_p, v);
This plots all the contour lines within this specified domain which is exactly the contour lines outside the circular domain, albeit, there are some lines that cross into the domain since the contour lines are continuous. In order to cover up these excess data points, I plotted a solid circle made up of hundreds of black circles. I did this by doing:
v = [-3.0:0.1:1.0];
t = linspace(0,2*pi,length(x));
contour(X, Y, C_p, v);
hold on
for i = 0:10000
xc = 0.0001*i*cos(t);
yc = 0.0001*i*sin(t);
plot(xc, yc, 'k');
end
hold off
I hope that this helps anyone else who runs into this problem in the future! Good luck community!