Religious leaders have stepped into the political fray in Eswatini — and it seems they’re hoping for a miracle of sorts: to get the protagonists in the country’s conflict around the negotiating table.

Swazi activists have long been pushing for a move from absolute monarchy to multiparty democracy. But with their demands more recently turning to outright deposition of King Mswati III, they’re likely to meet intransigence on that count, at least...