The James Webb Space Telescope (JWST) Cycle 1 call for proposals now includes opportunities for Archival Research (AR) proposals of targets in the Guaranteed Time Observation (GTO) programs that have no exclusive access period – a full list can be found here:
https://tinyurl.com/y7kqsj7c 

Most available programs include Solar System objects and details of these observations can also found through the link provided. The JWST AR Program can provide financial support for U.S. scientists for the analysis of such data sets. AR proposals must outline a management plan and detailed budget for analyzing the data. Proposals for Archival Research are considered at the same time, and by the same reviewers, as proposals for observing time, on the basis of scientific merit.

The JWST Cycle 1 Proposals are DUE April 6, 2018 at 8pm Eastern Time.

The full call for proposals can be found here:

https://jwst-docs.stsci.edu/display/JSP/JWST+Cycle+1+Proposal+Opportunities