We recommend an oil-based finish such as General Finishes Arm-R-Seal.
Oily woods can be tricky with any topcoat. The high oil content affects the drying process of the finish coats and Padauk has a very high oil content. Sometimes oily woods dry fine and sometimes they take weeks.
Try wiping the wood with alcohol or acetone to dry the oils before coating. This technique may help but does not work all of the time - each piece of wood is different.
To be safe, always plan on a long dry time.