  This paper is a continuation of our earlier work "[T. Jin, Y.Y. Li and J.
Xiong, On a fractional Nirenberg problem, part I: blow up analysis and
compactness of solutions, to appear in J. Eur. Math. Soc.]", where compactness
results were given on a fractional Nirenberg problem. We prove two existence
results stated there. We also obtain a fractional Aubin inequality.
