McConnell, 27, was sentenced to 20 weeks in prison, suspended for 12 months, after being found guilty of attacking the former Hollyoaks actress.
Miss Davis told the trial she thought that "psychotic" McConnell was "going to kill" her after taking cocaine.
McConnell was also ordered to complete 200 hours community service.
Miss Davis, 24, said McConnell threatened to throw acid in her face during the drink and drug-fuelled bust-up at her home in Rainhill, Merseyside, on March 10.
McConnell, from Swords, in the Republic of Ireland, first met his former partner after they appeared together on Celebrity Big Brother.
He had denied the attack, branding Miss Davis a "blatant liar", but was convicted of assaulting her during a trial on Monday at Liverpool Magistrates' Court.
The court was shown photos of a bruise that Miss Davis said was caused by McConnell biting her arm, as well as extensive bruises to her legs and body, said to be caused by punches.
Passing sentence District Judge Wendy Lloyd told McConnell he had shown no remorse and attacked his ex as she held their baby in her arms after he had taken alcohol and cocaine.
She told him: "If you get yourself into such a state then you have to accept responsibility for it."
Judge Lloyd also imposed a restraining order on McConnell for three years, banning him from contacting Miss Davis except through intermediaries and for the purpose of contact with their child.
James Morris, defending McConnell, told the court  about the Dubliner's tough upbringing and a series of personal family tragedies.
Mr Morris said: "Mr McConnell clearly has had a number of demons in his past that needs to be addressed."
He added: "It's fair to say this was a volatile relationship where accusations of infidelity reared their ugly heads on a regular basis."
The court was told the defendant had attended a private rehab clinic in Ireland to be treated for "chemical dependency" and he was now free of cocaine use.
In a victim impact statement read to the court, Miss Davis, who was not present, said the attack had left her a "nervous wreck".
She said: "I feel like I'm drowning...I feel numb inside and just want this nightmare to be over."
Reality TV star Jeremy McConnell has been given a suspended prison sentence for assaulting his ex-girlfriend Stephanie Davis.