Coverage of Web of Science The reason I'm asking this question is that I've never used Web of Science before. My apologies if it is silly or irrelevant.

I'm gathering materials for an application to a tenure-track job, and one of the things I have to submit is a list of my publications as indexed in WoS. This is an important thing for them, because they make it clear in the call for applications that those publications that are indexed in WoS are going to count more that those that don't (they do it this way because the call is division-wide, not department-specific, so they use WoS as a scholarship quality metric that doesn't require the members of the search committee to be experts in the specific fields of the candidates). 

WoS behaves well in that, if I query my name and field, it returns all of my journal publications, including a couple of obscure book reviews I did in my first year of grad school. On the other hand, it also behaves badly in that it fails to return anything that is not a journal publication. This bothers me because I have a couple of book chapters with reputable presses (e.g., OUP) and proceedings of high-profile conferences that my peers and mentors acknowledge are as important (in terms of quality and contribution to the field) as any of my journal publications; but because they don't appear in WoS, the search committee will view them as second-rate publications.

The question is, is there a way I can make WoS index these publications?
Web of Science is terrible in coverage of many fields (not sure what yours is from the post), and if you're stuck with it, you're stuck with it.  Try to see if there's anywhere that you can also say, "and here are my important publications that WoS doesn't cover, and here are all of their many many citations..."