The players, who are not related, must file a appeals for Hennepin County Judge Gary Larson's stay to kick in, the (Minneapolis) Star Tribune reported. They face four-game suspensions for taking banned substances.
Larson ruled earlier this month that the NFL violated Minnesota labor laws when the Williamses were tested. But he found the violation did not harm them and said the suspensions could be imposed.
The judge said Friday he believes the players will win their appeals.
"We're confident ultimately the courts will determine when an entity like the NFL violates a public policy statute, it can't proceed unrestricted," said Peter Ginsberg, the lawyer representing the players. "Until the NFL conforms its procedures to state law, it will no longer be able to act unilaterally and, we think, irresponsibly."