∵⊙O1和⊙O2相切,两圆的圆心距为9cm,⊙O1的半径为4cm,
∴若外切,则⊙O2的半径为:9-4=5(cm);
若内切,则⊙O2的半径为:9+4=13(cm),
∴⊙O2的半径为5cm或13cm.
故选D.