The question as posed is impossible to answer.
Reasons:
Israel was the Northern Kingdom and Judah was the Southern Kingdom. As a result it is hard to tell which one you are referring to when you say "The Southern Kingdom of Israel".
Secondly the Kingdoms of Israel and Judah reigned for a few hundred years and therefore had many kings. Without specifying an exact event or year or period, it would be impossible to know which king you want to know about.
King David was the king of Judah and Israel. The separation between the kingdoms was on the days of king David's grandson, king Rehoboam (son of king Solomon, who was the son of king David).
The southern kingdom of Israel, known as Judah, consisted of two tribes: Judah and Benjamin. This division occurred after the united monarchy split into the northern kingdom of Israel and the southern kingdom of Judah following the reign of King Solomon. The tribe of Levi was also present in Judah, serving in religious roles, but the primary tribes associated with the southern kingdom are Judah and Benjamin.
While King Solomon reigned there was peace, but when he died the peace had stopped. The kingdom then split to the north half Israel and the south half Judah. The Northern part, Israel, eventually turned to polytheism and was destroyed by assyria, while the Southern part continued to believe in one God, and their faith was renewed by the prophets.
He annointed the boy David as king of Israel.
King David
King David was the king of Judah and Israel. The separation between the kingdoms was on the days of king David's grandson, king Rehoboam (son of king Solomon, who was the son of king David).
Today there is no king of Israel.
The Negev Desert is in southern Israel.
Hoshea was the last king of Israel.
The Negev Desert is found in southern Israel.
The northern and southern kingdoms of Israel divided around 930 BC, after the death of King Solomon. This division was a result of political and religious tensions between the tribes of Israel. The northern kingdom became known as Israel, with Samaria as its capital, while the southern kingdom became known as Judah, with Jerusalem as its capital.
The Negev Desert covers most of the southern half of Israel.
According to the Bible, General Jeroboam led a successful secession from the Unified Kingdom of Israel under King Rehoboam, leading to the creation of the Northern Kingdom of Israel under King Jeroboam and the Southern Kingdom of Judah under King Rehoboam. (Yes, the entity that seceded kept the name.)
Saul was Israel's first king.
jehu
As king, he had none. Saul was the first Hebrew king.
The Negev is located in southern Israel. See the attached Related Links for a map.