I'm not sure if they would consider it as 'excess baggage' in which case, the following may apply;
"Excess Baggage
Subject to availability and at Jet2.com's discretion you may check-in excess baggage, which will be subject to an additional charge. This is currently 10GBP / 14EUR / 20CHF / 360CZK / 55PLN per kg and the charge is payable at the departure airport. Payment is generally accepted in local currency cash or by payment card which support foreign currency transactions. If you are planning to travel with excess baggage please allow extra time for the check-in process. No single item of baggage may weigh more than 25kg, with the exception of certain items of sporting equipment which may weigh up to 32kg."
It would be worth giving them a call to check.
Not sure how old the baby you are travelling with is, but when Ryan was younger, we used one of these; https://www.boots.com/en/Samsonite-Pop-Up-Bubble-Travel-Cot-Cafe-Creme_13852/ - and that fit inside my suitcase with plenty of room. EDIT: It was the smaller version of this.
Will they not provide travel cots where you are staying?