Thank you Casalguidi for the record! This is certainly seems to be the Daniel Horatio we were looking for! Hello "Cousin" Ausseabreeze! Thank you Richard for your continued assistance.
A summary:
A five year old Daniel Horatio Friend was in the 1851 census with George Marshall Friend and Elizabeth Friend, and listed as their grandson. We wished to find the parents of Daniel Horatio. We could not find a record on IGI or the FreeBMD. We knew the children and other grandchildren of George M. and Elizabeth, but Daniel H. was not accounted for! One son of George and Elizabeth was Capt. Daniel Friend. Daniel died at sea in 1848 and his will was later contested in court. Thanks to this website, we were able to read about the court case. The record revealed that Daniel willed half of his estate to his mother and half to his (quote) "Eliza my niece/adopted daughter". Their shares were then to revert to his illegitimate son on his 21st birthday. The will was contested because the law did not allow for the heir to be an illegitimate child. This child happened to be the age of Daniel Horatio.
The will did not mention any wives nor any other children of the Captain. We were unable to find any marriage records for him either.
Capt. Daniel did have a niece named Eliza. She was the eldest child of his oldest brother George. We had her baptism record and Casalguidi has repeated it above.
An intelligent conclusion of reading the court case is that his niece Eliza was the mother of his illegitimate son. Why else would a "niece/adopted daughter" receive half the estate when none of the other nieces and nephews of the Captain received anything; and why would her share then revert to the illegitimate son, if she were not the boy's mother? The age of the illegitimate son matches the age of the Daniel Horatio in the census. This Eliza was 15 years 9 months old at the birth of Daniel Horatio. If this was an indiscretion of the Captain, such indiscretions are not unheard of.
As mentioned above, we had no baptism or birth record for Daniel Horatio until Casalguidi's post. This record is a match in name to the 1851 census and a match to the age in the 1851 census. Also, the birthplace of Deptford is the longtime hometown of grandparents George and Elizabeth. Finally, the listed names of the parents, namely Daniel and Eliza, are extremely interesting considering that the hypothesis from the court case is that the parents of the illegitimate child are Capt. "Daniel" and his niece "Eliza". The deduction is that Daniel Horatio is the illegitimate child.
Eliza would go on to later marry Thomas Liversuch Noon.
