Babylist.com accepts Klarna as a form of payment. You can see if your Babylist order qualifies for Klarna here.
If the items you're wanting to purchase are sold by other retailers, the retailer will have to offer Klarna as a payment option to use it. Klarna is accepted by thousands of online retailers. You can see more Klarna stores here. If the retailer doesn’t offer Klarna, you will not be able to use Klarna as a payment option at that store.