I have used the Abaqus built-in anisotropic hyperelastic models with the built-in linear viscoelastic model, so I am not sure that combination works. I suspect it will, but you will need to read the manuals to find out. I know that combination works, for example, in ANSYS.
You will very likely need to manually edit the inp-file to make it work.
Also, the PolyUMod library supports these features, and you can use the trial version to check it out.
Jorgen Bergstrom, Ph.D.