They said they were concerned that religious worship is being neglected, because young people are afraid to miss their sporting pursuits.
The bishops want to see players, officials and coaches at Mass instead.
"Dedicated young sports people can be afraid to miss a training session or a game, for fear they will lose their place on the team," the bishops said, in a statement issued on the second day of their annual spring meeting.
"When practice sessions or competitions occur repeatedly on Sunday mornings, then a young participant can lose the habit of going to Sunday Mass," they warned.
Last night a spokesman said that the bishops hope their new campaign "to keep Sunday morning as a sacred time" will receive a positive response from the GAA, as well as from soccer and rugby club organisers.
But the Irish Rugby Football Union and the GAA both rejected the appeal as logistically impractical. The Football Association of Ireland did not respond to the bishops' plea.
According to the bishops, until recent times, Irish Catholics observed a traditional balance, whereby sporting and leisure activities for young people on Sundays did not begin until early afternoon.
But they warn that this observance of Sunday as a special rest-day has been affected by the ever-increasing frequency of scheduling under-age training sessions and competitive games for Sunday mornings.
"This conflict of interests becomes all the more acute for a multi-talented youngster, since he or she may wind up with a non-stop round of Sunday morning engagements."
The bishops also warned Catholic parents and guardians that they may lose sight of their responsibility of attending Sunday Mass because they need to travel with young people to events.
"It is sometimes claimed that a young player or a family can go to the Saturday Vigil Mass in advance of a Sunday morning engagement," the bishops continue, pointing out that for any number of practical reasons, this may not always be possible on any given weekend.
But GAA spokesman Danny Lynch said that while the organisation had noted the bishop's comments, it would not be logistically possible to cease all training and matches on Sunday mornings.
"We have 20,000 teams which means 10,000 games. We have matches and training sessions right through mid-week and on Sunday and Saturday mornings and afternoons," he said.
Impractical
An IRFU spokesman also dismissed as impractical the suggestion that play and training cease on Sunday mornings.
"It is not practical from an organisational or logistical point of view," he said, adding that match and training times were entirely at the discretion of each club. While games are more usually scheduled for Saturday and Sunday afternoons, in order to ensure access to pitches, Sunday morning play was necessary as well, he said.
In their statement, the bishops also expressed concerns about young people in part-time weekend jobs who have to work both Saturday evenings and Sunday mornings, without time off to attend either a Vigil or a morning Mass.
The bishops also point out that they share the concern raised by healthcare experts about the increasing numbers of children who do not engage in any physical activities or pastimes. the bishops also praised adults who voluntarily give of their own free time to promote sporting and other creative pastimes among young people.
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