There are many good airfoils to choose from but none of them will work well on a wing which has one part of the wing working against another part. To get good results the washout along the wing has to be coordinated with the taper and sweep to get an efficient lift distribution. This is far more important than which good airfoil you select. See:
http://aero.stanford.edu/WingCalc.html
Put your planform into this online program and try various washout angles to see which gives the best results over a range of angles of attack and lift coefficients. The closer the "e" number is to 1.0, the more efficient the lift distribution. The airfoil you choose has to be capable of the coefficient of lift without stalling.

To choose an airfoil, go to:
http://soaring.cnde.iastate.edu/calcs/frames.shtml
There you can compare the polars of up to five airfoils at once to find an airfoil that matches the coefficient of lift range for your wing design and the flaps up speed range you are looking for.

Working back and forth between these two programs can allow you to refine your design.