Are the objects roughly circular? That'd make it somewhat easy, since the intersection will always happen at the same distance from the middle point.
cos(angle(obj1.x, obj1.y, obj2.x, obj2.y))*obj1.radius
sin(angle(obj1.x, obj1.y, obj2.x, obj2.y))*obj1.radius
It's not a perfect solution but it's simple and will likely do the trick for what I'm assuming is a suika style game.