I don't know all of his cousin's names, but i do know that his 7th cousin is someone by the last name of Brewington. I am not sure if the relation is by marriage or not. Hoped this helped, probably not, but at least it is something.
Presuming you are asking about 1st cousins, then the offspring of Abram (Abraham's) father's children would fit. However, the main line that The Bible notes would be the line of 'Lot' who many biblical scholars match these descendants to the people in modern day Jordan (Arabs):
Genesis 11:26-32New International Version (NIV)26 After Terah had lived 70 years, he became the father of Abram, Nahor and Haran.
Abram's Family27 This is the account of Terah's family line.Terah became the father of Abram, Nahor and Haran. And Haran became the father of Lot. 28 While his father Terah was still alive, Haran died in Ur of the Chaldeans, in the land of his birth. 29 Abram and Nahor both married. The name of Abram's wife was Sarai, and the name of Nahor's wife was Milkah; she was the daughter of Haran, the father of both Milkah and Iskah. 30 Now Sarai was childless because she was not able to conceive.
31 Terah took his son Abram, his grandson Lot son of Haran, and his daughter-in-law Sarai, the wife of his son Abram, and together they set out from Ur of the Chaldeans to go to Canaan. But when they came to Harran, they settled there.
32 Terah lived 205 years, and he died in Harran.
Abrahams challenges were that he had to protect his kids.
Doris Abrahams was born in 1921.
Sidney Abrahams died in 1957.
Sidney Abrahams was born in 1885.
Israel Abrahams died in 1925.
Israel Abrahams was born in 1858.
Bennie Abrahams died in 1990.
Bennie Abrahams was born in 1907.
Ottilie Abrahams was born in 1937.
Peter Abrahams was born in 1919.
Chris Abrahams was born in 1961.
Carl Abrahams was born in 1911.