Wakefield Prison guards are among those being asked to become mentors for young people in care.
A service run by the charity Barnardo's, which matches volunteers with youngsters in the care system, is in desperate need of more men to take part.
A report put before local councillors on Wednesday said that hiring people to help mentor children has become "very difficult" for Barnardo's, following a muted response to recent volunteer recruitment fairs.
Super League club Castleford Tigers are among the organisations who've been trying to help by sharing adverts, while leaflets have been handed out to male staff at local prisons.
Kate Pearson, who works for Barnardo's as the service's team manager, discussed the issue at a corporate parenting committee meeting.
She said: "We're carrying on with what we've done, but it's very hard work. It's the area where we put the most amount of our efforts into.
"But I think it's a national issue, getting men to volunteer with children.
"We did have two men quite recently who were interested, but unfortunately they changed their minds."
Among the typical duties mentors are asked to perform are helping their young person write letters, attending fostering meetings with them and offering themselves as a role model.
All volunteers are given specialist training.
Feedback from children who have been paired with mentors, or "advocates" as the adults are known under the scheme, has been overwhelmingly positive.
Around 85 per cent of youngsters surveyed said having an advocate made a positive difference to their lives, while more than 90 per cent said they felt "listened to" as a result of the project.
Councillors suggested targeting barbershop waiting rooms and local Men In Sheds groups for further recruitment.
Councillor Jacquie Speight said: "I know there's been a lot of hard work put into all this. Sadly, it does seem to be national issue where men don't appear to see themselves as a mentor to children as much as women do."
Anyone interested in becoming an advocate can visit https://www.barnardos.org.uk/what-we-do/protecting-children/childrens-rights-advocacy
Local Democracy Reporting Service