How to set covariance for Bivariate Logistic Distribution
The covariance of any multivariate distribution is always a matrix. Maybe it is of help to you to know what this matrix contains:

-In general, each entry i,j of the matrix gives you the correlation between the RVs i and j. 

-So a diagonal element i,i will simply be the variance of the RV i.

-If RV i and j are independent, then the non-diagonal entry i,j is zero (they are uncorrelated). The reverse of this statement is not generally true, but it is for Gaussians iirc. 

I don't know what you are trying to do, but perhaps the trace of the matrix or its determinant is of use to you?