The newborn boy is 10/1 to play in the Premier League like his father, but with far longer odds to turn out for either of his teams.
Klay is rated 50/1 with Ladbrokes to appear for Manchester United, 100/1 to play for Everton and the same odds to earn a senior England cap.
The bookmaker also offers odds on the Rooneys continuing the trend of baby names beginning with K, having also named their first son Kai.
Punters can get 5/4 on the third Rooney child following suit, or 4/6 on Wayne and Coleen opting for a name beginning with a different letter upon having another baby.
Any member of the Rooney family advertising Special K cereal is rated at 20/1, while the following names are all given long odds:
- Kourtney 25/1
- Karter 33/1
- Kassius 40/1
- Kris 40/1
- Khloe 50/1
- Kim 50/1
- Krystal 66/1
- Kristy 66/1
- Kanye 80/1
- Keith 100/1
- Kevin 100/1
- Kallum 100/1
Coleen Rooney has tweeted a picture of her second son Klay, who was born earlier today.
Coleen Rooney's mother Colette Mcloughlin has arrived at Liverpool Women's Hospital to greet the family's new arrival.
Accompanied by Wayne and Coleen Rooney's now-eldest son, three-year-old Kai, she brought in balloons to celebrate the birth of Klay.
Wayne Rooney missed Manchester United's last game of the season against West Bromwich Albion on Sunday to be with his wife as she prepared to give birth to their second child.
Coleen Rooney, wife of footballer Wayne Rooney, has tweeted to say that she has given birth to her second child, Klay Anthony Rooney.
Already mother to three-year-old son Kai, she said the family was "happy and doing well".
At 2.11am our Beautiful Son .... Klay Anthony Rooney entered the world. He weighed 7Ib 11.1/2 oz We're all so happy and doing well. X
Wayne Rooney also tweeted, to say the whole family was "delighted".
Our Beautiful Son Klay Anthony Rooney was born at 2.11am, Weighing 7Ib 11.1/2 oz. Both Klay and Coleen are fine..... We're all delighted!!