Added Ann Maria Hancock's parents William Hancock and Susannah Grigsby.

I've never been able to find any reference to a son James to James Muncaster and Rachel Ann Gray, so I deleted him. Everything I've found shows sons Zachariah who went to Montgomery Co, MD and John who went to New Orleans and three daughters: Rachel, Sophia and Sarah.

My grandfather wrote an article on Muncasters in Maryland which confirms that James Copper Muncaster married a Hancock:

There seem to be no family records of the Muncasters of Maryland and the story is very 
incompletely gathered from the court records of the province of Lord Baltimore and the State of 
Maryland.

The first mention known is the record of marriage of James Monkister to Elizabeth Charmion in 
1671. She owned some land in Charles County Md. and at her death it passed to her son William 
Monkister. In later records her name was spelled "Shearman" and his became Muncaster as it is 
now spelled. 

William lived from 1675 to 1717. In 1707 he patented a tract called "Muncaster Croft", 100 
acres. This seems to be all the land he ever owned though his wife's land was added to this. 
The next owner was William Muncaster (1702-1750) and when he died it descended to his son James 
(1735-1805) and the plantation had grown to about 400 acres at the time of his death. James 
left it to his four children: Zachariah, John, Sarah and Sophia. He had another daughter 
Rachel, but she had married Walter Stone of Frederick Co. against his wishes and he left her 
out of his will.  John (1769-1829) bought the shares of his brother and sisters in the farm in 
1810, paying them 541.71 apiece. He lived on the farm. In 1796 he married Elizabeth Copper who 
owned property in Alexandria, Va. His brother Zachariah was married in 1804 and moved to 
Montgomery County where his wife Harriet Magruder owned a 200 acre farm and a group of slaves. 
Their descendants are found in Montgomery County, Md.

In 1819, John sold his farm and everything on it, and moved his family (wife and five children) 
to Louisiana, settling in Carrolton, near New Orleans.  Charles Wallace, Christiana, Cyrus 
Copper and Harriet Sophia reached New Orleans, a daughter, Mary was born afterwards, and a son 
Dr. James Copper was left at Henderson, Ky. where it is said to have married a Miss Hancock and 
set up the practice of medicine.  He was about 22 years old and he held a diploma from Medical 
College of Maryland, and license to practice in that state granted in 1818. 

He practiced medicine in Henderson until his death in 1829, when he left a widow and three 
children, but there is no record of their names, and they seem to have been lost to the 
Maryland family until about 1877 when a letter from the oldest son gave the names of his 
children as John, George, Thomas and three girls whose names he did not give. From this 
descendants have been traced in Kentucky, largely up to date.

The other fact matching up is that the 1850 census shows Annah living in KY but being born in VA as was Ann Maria.

On May 30 I got this email from Jim Davis:

Hello
Hi how you i am doing just fine
I need you to check this out
I found  a  ANN MARIA HANCOCK  WHO MARRIED JAMES C MUNCASTER   COULD SHE BE THE ANNAH
Please check this out on ROOTS WEB WORLD CONNECT ON NORTHRUPS / NORTHORPS/GALLOPS  AND FAMILY

I got on Rootsweb and found William Hancock born about 1765 in Virginia, died 1827 in Henderson Co, KY.  Oct 27, 1788 he married Susannah Grigsby (born about 1767) in Fauquier Co, VA.  It shows them having 4 children, one of which was Ann Maria born about 1800 in VA who married James C. Muncaster born about 1798.

The only thing I really have on Annah is the 1850 census for Henderson Co, KY which shows her living with her son John W.  He was born June 22, 1821 in Henderson Co, KY.  The date is consistent with what we have on Ann Maria Hancock and we know the Hancocks and James Copper were all in Henderson Co, KY, so it is likely that this Ann Maria Hancock is the same Annah, but I can’t tell for sure.