While I don't think that I would trust a FindCopula function, there's no need for a FindCopulaParameters because FindDistributionParameters already provides that functionality. Here's an example:

d = CopulaDistribution["Product", {GeometricDistribution[\[Lambda]1], PoissonDistribution[\[Lambda]2]}];
n = 1000;
SeedRandom[12345];
x = RandomVariate[d /. {\[Lambda]1 -> 0.3, \[Lambda]2 -> 4}, n];
mle = FindDistributionParameters[x, d]
(* {\[Lambda]1 -> 0.304507, \[Lambda]2 -> 4.057} *)

And another:

d = CopulaDistribution[{"FGM", \[Alpha]}, {NormalDistribution[\[Mu]1, \[Sigma]1],
  NormalDistribution[\[Mu]2, \[Sigma]2]}];
n = 1000;
SeedRandom[12345];
x = RandomVariate[d /. {\[Mu]1 -> -1, \[Sigma]1 -> 2, \[Mu]2 -> 1, \[Sigma]2 -> 1/2, \[Alpha] -> 0.2}, n];
mle = FindDistributionParameters[x, d]
(* {\[Alpha] -> 0.221636, \[Mu]1 -> -1.04899, \[Sigma]1 -> 1.99398, \[Mu]2 -> 0.996975, \[Sigma]2 -> 0.481067} *)

But FindDistributionParameters for all distributions suffers from not giving an estimated covariance matrix for the parameters estimates. For that you'll need to write your own using LogLikelihood and something like FindMaximum.