Look at the aluminium polymer electrolytic section. They are more expensive than the classical electrolytics, but you'll easily meet the spec. You'll likely still need to get "excess" capacitance to meet the ripple current requirement, but usually nothing wrong with that.
OTOH, 10uF at 56V is doable with ceramics, then the current rating won't be an issue. This would be around 40uF nameplate capacitance with 63V rated X7R ceramic caps in 1206 or 1210 case, so you'll need to parallel many, for example 15-20pcs of 2.2uF nominal will likely do. Be very careful avoiding board flex and excessive soldering heat, though. And while using assumptions (like I showed) is OK for first order approximation, do look at the DC bias curves for the particular capacitor you are going to buy. Some are down to 15% at rated voltage, some are still at 30, even 40%, even if both have the same X7R dielectric rating.