20-Year Prospect
With the increased amount of states absorbing this position into other branches of their legal system, the twenty-year projection for this position is not looking so good. As of this year, only five states (CT, MA, NH, SC, and VT) are still actively seeking justices (source).
If you're lucky enough to live in one of those states or are willing to relocate and establish yourself quickly, you just might be able to snag a position while it's still available. The question you'll have to ask yourself is whether or not it's really worth it to set your goals on a career that's on the brink of extinction.
In either case, having a backup plan is highly advisable. Maybe you'll continue on in law and become a judge or delve deeper into politics and run for local office. Considering the type of qualifications needed to land the role of Justice of the Peace, you'll be well pre-pared to take on other avenues in the legal and political sectors.