Student assignments, and even individuals interested in doing JE translation usually start from the proviso – select a story that hasn’t yet been published in English.
The standby source used to be the Japan Foundation’s Japanese Literature in Translation database. It doesn’t provide full coverage – you will find some translations missing – but it is pretty darn good.
Allison Markin Powell maintains a database called Japanese Literature in English. It is definitely worth your time to check both the Japan Foundation database as well as Powell’s.
David Boyd pointed me to the 3% Database, which used to be housed at the University of Rochester and maintained by Chad Post is now available through Publishers Weekly. Translation Database . One unique feature of this database is that you can search by the gender of both the author and the translator.
For the purposes of aspiring translators, rather than student assignments, David Boyd kindly pointed out another excellent source of information from Japan Foundation – an annual list of which books were awarded translation and/or publication funding support. I hadn’t realized that this source of information was so useful, but it really is and it is worth checking all the regions because some really good English translations are coming out from all kinds of countries. Support Program for Translation and Publication on Japan