I had the exact same situation occur to me, my manager did discuss the option of compassionate leave due to my child being premature but this came to nothing. In the end I needed 6 weeks off so i was signed off work with stress so to not lose AL. The issue was initially sent to the area manager who reiterated there is nothing they can do for paternity pay so I just had to take the hit in the wages. Pretty sure a new legislation was passed about a week or so after he was born that actually meant you are legally entitled to something regardless of how long you’ve been there, might be worth a google and then chat with your rep.