Hi again,
Well, the other amp you posted is a little better, having a current boosted voltage follower output stage. That's only got about 1 diode drop, which isnt bad really. That should work too without going to too much trouble.
You should be able to get this to work one way or another. You'll have to remember though that with a 12v power supply putting out a sine wave without using a bridge arrangement will mean only 6v peak is available even with a rail to rail device. That's only 0.6 amps peak into a 10 ohm load too.
With a bridge arrangement you can get 12v peak with a rail to rail, or about 10 or 11v peak with a standard transistor output. That's about 1 amp peak into a 10 ohm load.
For a bridge arrangement you build two such circuits and invert one of them with the op amp or another op amp. You then connect between the two outputs rather than between output and ground. That gives you twice the output voltage peak that you would get from a single output amplifier.