Sampling from a couple of negatively correlated gamma variates

We propose two algorithms for sampling from two gamma variates possessing a negative correlation. The case of positive correlation is easily solved, so we just mention it. The main problem is the lowest value of the correlation coefficient that can be reached. The starting point of both algorithms is generation from a bivariate density with uniform negatively correlated marginals. Actually the first method uses a degenerate bivariate density since it considers two uniforms related by a linear relationship. Then we resort essentially to the inverse transform method. For both algorithms we stress restrictions on the parameters and rigidities.