The four bright Galilean moons of Jupiter, Io, Europa, Ganymede and Callisto, and their shadows, along with the position of Jupiter's Great Red Spot (GRS).
Show events for hours. Recalculating ...
Galilean is a "progressive web app", meaning that you should be able to install it on the home screen of Android or iOS phones and tablets. It doesn't collect data or need any funky permissions, and shouldn't need to use the network at all once you have the images downloaded.
Times are approximate. Jupiter's edge is fuzzy (you're looking at the tops of clouds), and models vary on exactly when transits begin and end. Models for eclipses vary, too. Start observing ten or fifteen minutes early if you want to be sure of seeing an event.
For older Java "dumb-phones", Miguel Moreto has adapted the older Java code for an app called Mobile Jupiter.