Aside from water, are there any other liquids I can use to stew tomatoes to make a purée?
I was thinking maybe chicken stock or vegetable but don't know how that would taste or if it would even be worth wasting stock unless the flavor would be very significant.
Has anyone tried?
If your goal is indeed a sauce or purée, you will want to reduce the total amount of liquid in your tomatoes, typically by reducing the sauce, i.e. boiling the liquid off.
Any additional liquid simply extends the time required unless you add a liquid explicitly for taste, e.g. red wine, a dash of (balsamic) vinegar or broth. Wine for example does influence the flavour profile even in small quantities, stock (depending on concentration) might require quite a large amount to be noticeable and therefore you need to reduce the sauce much longer. Whether this is good for your final product (long simmering to melt flavours) or bad (loosing the "freshness" of your tomatoes) is impossible to say without a recipe or knowledge about the expected results.
If your recipe (or your cook's experience) doesn't call for any addition of this kind, you may use a very small amount or omit the water altogether.
You want to chop (optional: de-seed or peel) your tomatoes and heat them slowly at the beginning. This gives them time to release enough juice to prevent burning. Once you have enough liquid in your pan, proceed as usual.
