Whenever your business is disrupted by a major event in the life of an employee--such as the birth of a child--don't make the mistake of treating it as a problem and a headache. Instead, recognize it as a chance for the company to shine. You don't get a lot of those opportunities, and the triggering event isn't always a happy one. It could be a death in the family or a long-term illness. Your response to such circumstances will have a huge impact on your company's culture. Everyone will view your actions as a measure of how much you care about your people.
Of course, what you do will depend partly on the size of your business and partly on the particular circumstances of the employee. The general rule is: Come up with something outside the norm. Suppose, for example, an employee's wife gives birth. Maybe, in addition to paternity leave, you figure out how, afterward, the employee can work from home one day a week, or do his 40 hours in four days, rather than five.
Or if the mother is one of your employees, think about how you can help her out after her maternity leave. Six weeks isn't very long, after all. Perhaps, on her return, you let her work just three days a week at her full salary for a couple of months and ask the rest of the people to pick up the slack. You can frame it as their gift to her and her newborn.
To be sure, the employees' participation has to be voluntary. It's not a gift if people are required to do it. Most will probably be happy to chip in. If they aren't, you'll know something is amiss with your culture, and you'll need to address it. But chances are the experience will bind people closer together. That can't help but be good for your business.