Coulton, 20, spent time on loan at National League North sides Chester and Bradford Park Avenue last season, getting experience at a high level of men's football.
He is no stranger to the Northern Premier League, having featured on loan at Warrington Town during the 2021/22 campaign.
Joining him at Broadhurst Park is former Skelmersdale United forward Morris.
The 25-year-old can play across the frontline and steps up the divisions after impressing at his former club.
Both players go into contention for the Reds' upcoming pre-season friendly against Barrow on Saturday 8 July.
Photo credit: Preston North End