The FA plans to introduce what it calls "temporary dismissals" in England's step seven - six tiers below the National League - and the leagues below.
They will only apply to yellow cards shown for dissent, and will see players leave the field for 10 minutes.
It will also be tested in Sunday League and male and female youth football.
More than 1,000 clubs received emails over the weekend asking if they were willing to be part of the pilot process.
"There has already been a positive response with over 60 leagues in support of it," an FA spokesperson said.
Clubs are normally charged a £10 fine for each yellow card but the FA will not be charging this administration fee for those that participate.
Step seven is the bottom level of English football's National League System, which feeds into the country's professional leagues.
The highest league within that structure - step one - is the National League.
The move has been backed by teenage Sunday League referee Ryan Hampson, who earlier this year organised a nationwide strike by officials in protest at the amount of abuse they face in the grassroots game.
"There's obviously a lot more to be done but it's a step in the right direction and a great start," he told BBC Radio 5 live.

Hamilton finished third as Mercedes team-mate Nico Rosberg won and is 33 points behind the German with a maximum of 100 still available.
The world champion said: "That's a healthy margin for Nico. He did a great job so congratulations to him.
"It is going very well for him. I just have to try to do the best job I can."
Rosberg's ninth victory of the season means he can now afford to finish second behind Hamilton in all the remaining races and still win the championship.
Hamilton made a bad start from second place on the grid and fell to eighth on the first lap but fought back to finish behind Red Bull's Max Verstappen.
Hamilton is flying back to Europe with Mercedes team boss Toto Wolff and non-executive chairman Niki Lauda.
But Wolff said the flight was not the right time to address with Hamilton the series of media controversies in which he found himself embroiled at Suzuka.
Wolff said: "Just after such a race is not the right moment to really put the finger where it hurts. We need to calm down and regroup.
"My learning from the last couple of years is that 24 hours later things look kind of different than they are here an hour after the race.
"So our main emphasis will be on building him up and just enjoying the ride home. And we have 10 days before [the next race in] Austin and he will come back stronger there."
Wolff rejected suggestions that the title was now as good as won for Rosberg, who has won three of the past four races and benefited from Hamilton's engine failure while leading in Malaysia a week before Japan.
Without that retirement, Hamilton would be two points behind Rosberg.
"Thirty-three points is a lot but you can see how quick it goes," Wolff said. "The way Nico is approaching the championship in taking each race as a singular event is the right strategy for him.
"Equally, Lewis functions best when he is under pressure and has a target. I have no doubt it is going to be an intense fight to the end. But it is far from over."
Rosberg said: "My thoughts are that my approach is going quite well at the moment, of just looking at the race at hand.
"I came here to win and I managed to win, so I'm really happy with that.
"Of course I am well aware of the 33 points but there is still a long way to go.
"And Lewis is still Lewis and he is always going to be tough to beat.
"He is going to give it everything so there is no point to start thinking about that because it is working quite well to stay in the moment."
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The Football Association will trial 'sin bins' in the lower leagues of English football from next season.
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Lewis Hamilton says he will give the remaining four races "everything I've got" after a major blow to his title chances at the Japanese Grand Prix.