To tell the truth, the only way to mount tires on alloy rims is by foot. After having too many rims and tires ruined by tire-jockey's I now do them myself.
Yes, it is a bit of work. But you wont ever have gouges in the lips of the rims, or torn beads, or... whatever damage.
By foot I mean that I walk them on with my feet. Put on a pair of sneakers, then a moving quilt or heavy towel on the driveway, some lube/sealant on the bead, and walk them on.
This isn't easy to describe (I need to get a picture or two), there is a "drop center" on the rim. Take a bare rim and set it upright in the same position as if it was on a car.
Then look at it directly from the front or back (as if it were on the car). Note how there is a section of the rim between the tire bead area that is smaller in diameter. That is the drop center.
Once the tire is over a portion of the rim, place the tire bead into this drop center. The effectively makes the rim smaller in diameter and allows the other portion of the bead to easily drop over the rim.
Then walk around the tire bead pushing it over the rim. Once one bead is on the do the other tire bead from that same side. It is best to push the tire on from the side of the rim that is closest to the drop center.
After they are mounted and inflated I put a few miles on them (25 - 50). Obviously around town since they aren't balanced yet. Then pull the rim/tires off the car and take them to someone trusted to balance them. Back on the car & good to go.
RemoveBeforeFlight