The Saundersfoot Railway's coastal line, which carried coal from Stepaside to the harbour from 1834 until 1939, is now part of the Pembrokeshire Coast Path. It runs from Saundersfoot past Coppet Hall and through three short tunnels to the hamlet of Wiseman's Bridge, about a mile with no real gradient, so it works with a pushchair. You can carry on another three-quarters of a mile to Amroth.
The cliffs here are unstable. The stretch between Coppet Hall and Wiseman's Bridge has been closed several times since late 2023 by rock falls, reopened after stabilisation work, and closed again; check with Pembrokeshire County Council before you set out.