If say a snake mostly feed on birds or eggs, definitely it will show as high contents of e.g. keratin (bird feathers) or calcium (e.g. eggs), as those excess chemical componds may be excreted. But that there wll be a molecule for e.g. rat, versus a lizard, am not sure - so one need to know what particular prey types consist mostly of, aside organic molecules such as proteins, amino acids, lips etc. that are common to many vertebrate prey. If invertebrates are fed mainly on, e.g. by small arboreal snakes such as the Green Tree Viper, their exoskeleton too may be indicative by high contents of Chitin (C8H13O5N)n or Silica (Silicium oxide) in faeces. So, if one want non-invasive dietary component-analyses then such trace chemicals may be indicative of whether birds or insects, or eggs. To distinguish mammalian prey types by faecal analysis seems to me problematic, but perhaps others may have some ideas here?

Identification to family or genera of skeletal remains in the faeces may be your best bet for a good portion of the diet. I'd talk to the anthropologists or archaeologists at your university as some archaeologists get really good at identifying species from limited remains.

Depending on your expertise and funding sources -

If you need to do this in the field with little funding see this paper: Article Notes on the diets of seven sympatric snakes in the genera A...

If you want to use DNA than this paper does a good job of comparing techniques and discussing the issues around using qPCR and HTS:

Article DNA-Based Faecal Dietary Analysis: A Comparison of qPCR and ...

This paper talks about using real-time PCR which might also be useful:

https://www.nature.com/articles/srep32166#materials-methods

Stable isotope work could give you a general sense of a species position in the food chain and what general type of food its consuming but I don't think would be a good choice if your looking to develop a species list of prey items.