Allen, 26, married husband Sam Cooper, a painter and decorator, in June, when she revealed she was pregnant.
Her friend Sam Chew tweeted Friday, "sending out love to lily, sam and mini cooper...... YES."
Actor Charlie Condou also tweeted his well-wishes, People magazine reported Saturday. Allen's representative had no comment on the birth.
Allen has had difficulties with pregnancies -- she lost one child in November 2010 after contracting a virus six months into the pregnancy and miscarried another in January 2008.
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