You can't. Courts are supposed to be above popular opinion.
With all due respect, the question was how to bring pressure, not how to influence via public opinion.
State supreme courts are very sensitive to the perception and opinions of higher federal courts. This sensitivity can be enhanced or 'pressured' by the specter of lawyers taking a poorly supported state supreme court decision to the federal level.
In fact, if the case has clear precedent, the federal courts could remand state court decisions with prejudice and possibly extreme prejudice. Such an event can be a career killer for state judiciary members.
How to take a state decision to the federal level is the question. Some say there are 14th Amendment grounds. It would be informative to discuss possible grounds for a federal hearing, just in case.