Software for computing Thurston's unit ball
"Better late than never." Stephan Tillmann and William Worden have produced the software package tnorm. This can be found here:
https://pypi.org/project/tnorm/
The software should be able to deal with hyperbolic two-component links easily. William replies to emails, as well. :)
I am not aware of any implementation. The best known algorithm is Cooper and Tillmann's, the closest (which is not very) to a table is in Curt McMullen's classical paper.