Hi Giorgie,
May is the start of the rainy season but it isn’t too intense that early on. You should read our post about the weather in Costa Rica (click here), which has data on number of days with rain and how much rain. For Manuel Antonio, look at the info for Puntarenas Province and for Tamarindo look at Liberia. Generally, you’ll have nice sunny mornings and maybe showers in the afternoon/evening on some days. May is a wonderful time of year to travel to Costa Rica- those two places are very popular so will be busy in January but a lot less crowded in May.