I think what you need is explained here, and without the use of copulas: https://www.r-bloggers.com/easily-generate-correlated-variables-from-any-distribution-without-copulas/

In the words of the author of the linked article (Francis Smart), the proposed method is:

> 1. Draw any number of variables from a joint normal distribution. 
> 
> 2. Apply the univariate normal CDF of variables to derive probabilities for each variable. 
> 
> 3. Finally, apply the inverse CDF of any distribution to simulate draws from that distribution.
> 
> The result is that the final variables are correlated in a similar
> manner to that of the original variables. This is because the rank
> order of the variables is maintained and thus correlations are
> approximately the same though not exact.

Hope it helps.