What record confirms that William Peter Coomes was the son of William and Rachel Coomes? This is what I have from the obituary of Felix Coomes, son of William and Rachel Coomes:
In the old Catholic prayer book, belonging to Mr. Coomes and printed in Philadelphia by James Carey in 1800, this interesting record is carefully inscribed on the fly leaf: "Register of ages-William Coomes was born March the 13th, 1769.Rachael Coomes was born October 9, 1775. Their children and their ages: Teresa Coomes was born September 7, 1797, Charles Coomes was born January 20, 1799, Elizabeth Coomes born October 1, 1800, William Coomes August 20, 1801, Mary Margaret Coomes, August 19, 1803, Enoch Ignatius Coomes born March 9, 1805, Charity Barbara born January 24, 1807, Felix Coomes born November 21, 1808, Benita Coomes was born October 10, 1810, Charity Coomes was born February 8, 1813, Stephen Coomes was born October 25, 1815 .This is the register of the family of Mr. Coomes' parents".
As you can see no William Peter b. 1818. William Coomes b. 20 Aug 1801 married Margaret V. Mattingly.