Apologies that nobody answered. Most researchers do indeed just use pre-compiled gene lists in order to infer cell-types in their data. Sometimes, employing an algorithm to do the work may not even be required, as certain cell-types are quite obvious, for example, scRNA-seq clusters that highly express CD56 are going to be on the natural killer cell lineage.
I believe a colleague recently searched for some programs that can infer cell-types 'de novo' without any pre-compiled lists; however, these are still going to be utilising some gene-to-celltype mapping in the background (and I cannot recall the name of the program).
As larger tissue-profiling studies are published and data is made available, I suspect that we will be able to, one day, predict most cell / tissue-types with high accuracy.
One of the earlier tissue-specific studies was actually from the FANTOM consortium, out of Rijken in Japan, and it was on this data that we constructed our own cell-type prediction algorithm for this work:
Molecular Portraits of Early Rheumatoid Arthritis Identify Clinical and Treatment Response Phenotypes
(I no longer work there).