Nice question!  I don't know of such a census.  Probably the first course of action is to email Damien Heard, the author of the program "Orb".  Here is the page for Orb.  

http://www.ms.unimelb.edu.au/~snap/orb.html

The documentation, a 13 page pdf file in the source code archive, is very helpful.  Basically, you want to draw a theta-graph, drill one of the edges, and label each of the other edges with a "2".  These graphs are in one-to-one correspondence with tangles (well, up to a Dehn twist about the equator of the tangle).

Orb can find canonical triangulations for these and can, it appears, use them to check for isometries.  This, in addition to its ability to compute volumes and length spectra, means it can deal with the filtering side of census building.  Orb can also compute two-fold branched covers, which will be handy.

I guess some version of DT codes will deal with the generation side of census building.  

Needless to say, this sounds like a non-trivial amount of work...

Postscript: I've be very interested to see how the two-fold branched covers of these tangles arrange themselves in the SnapPea cusped census.  Is there a way to directly "see" which elements of the cusped census have tangle quotients?