Ethics is always a touchy matter since different schools of thought are likely to arrive at different conclusions. Legally, if you are in a country that permits you to take two months of paternity leave, it is virtually certain that you are well within your legal rights to withold a desire to do so (particularly one which may or may not come to fruition) from a potential employer.
Practically, however, I would question the wisdom of your course of action. Off the bat, your employer seems to be telling you that its concept of work-life balance is at odds with the sort of balance you appear to want in your life. That sort of conflict is likely to appear throughout your tenure at this employer, not just if and when a second child arrives. What happens if you decide to take a day off to deal with a sick kid or you want to take a couple of hours off during the day to go to a prenatal appointment with your wife?
Your potential employer is also signalling that its approach to project management judges it reasonable from the outset to basically eliminate all slack in the timeline, including slack for things like vacation time, in a project with an implementation phase that stretches for two years. That is a pretty poor approach to project management that virtually guarantees that there will be more unrealistic assumptions and requests going forward. What happens if the scope grows or some component takes longer than they're expecting and they ask everyone to "pitch in" and work extra hours every week? If you take two months of paternity leave, are you going to find yourself blamed (rightly or wrongly) for any and all delays or failings in the project?
Even if you successfully navigate the legal and political minefield, after you devote yourself to a project that is already under severe schedule pressure for two long years, is it likely that the company is going to conclude that user18600 is a top notch employee that went above and beyond and reward you with a promotion? Or is it more likely that the company is going to conclude that user18600 doesn't fit in with the culture of the company, abandoned the team for two months, and only narrowly averted disaster? Given the signals the company is putting out, it seems highly likely that you'll have constant work-life conflicts and that the project is going to be a death march until it is either cancelled or limps across the finish line over budget, past deadline, and with less functionality that the users currently expect.