(Recasts with opening of trial, details on demonstrations)
DETROIT, Feb 25 (Reuters) - A lesbian couple's legal challenge to Michigan's voter-backed constitutional ban on gay marriage opened in federal court in Detroit on Tuesday, the latest in a series of trials brought by gay rights supporters in favour of marriage equality.
"This case is about marriage equality and it's about the well-being of children," Carole Stanyar, an attorney for the couple, who are both nurses, said in an opening statement.
"We would like this to be the last trial in America where same-sex couples have to defend themselves," Stanyar said.
Several dozen peaceful demonstrators marched in front of the courthouse.
Some supporters of the law carried signs that read "We Support Traditional Marriage - One Man, One Woman," while some opponents held signs urging the court to overturn the ban.
April DeBoer and Jayne Rowse, who live in suburban Detroit, are asking the court to overturn the state law that bars same-sex couples from marrying, and another that prevents them adopting each other's children.
The couple sued Michigan over the state's adoption law in early 2012 and later expanded their challenge to include the state's ban on gay marriage, which was approved as a constitutional amendment by voters in 2004.
U.S. District Judge Bernard Friedman waited for the U.S. Supreme Court to rule on cases that were pending before proceeding with the case.
In June, the U.S. Supreme Court threw out a key part of the Defense of Marriage Act, which denied same-sex couples federal benefits that are available to heterosexual couples. A separate decision allowed same-sex marriage in California.
In October, Friedman ordered a trial on the state's marriage ban and adoption law. Several courts around the country have struck down same-sex marriage bans since he ordered the trial.
Michigan's attorney general has said in court papers the marriage amendment voters adopted in 2004 is rationally related to legitimate state interests and marriage between one man and one woman is "uniquely suited to the rearing of children".
"There is no dispute that there is a fundamental right to marry," the attorney general said in court papers.
"But there is no fundamental right to marry a person of the same sex." (Reporting by James B. Kelleher in Detroit and David Bailey in Minneapolis; Editing by Ken Wills and Sophie Hares)