Try this:
1. Install one tire bead all of the way around.
2. Start installing the second bead exactly opposite the valve stem (important). Work around in both directions as far as you can.
3. When you run out of slack, go back to where you started and squeeze both beads into the center of the rim.
4. Now hold the wheel vertically in front of you with the valve stem near the floor. Grab the tire at the 3 O'clock and 9 O'clock positions and push straight downward. What you're trying to do is to accumulate all of the available slack at the unseated portion of the bead.
5. Using your hands attempt to seat the remaining portion of the tire bead.
Incidentally, a similar process also works for removing tires from the rim. I seldom have to resort to using tire levers.