I used to play it on my accordeon, so I tried to do it on the PSR3000. It tried some different chords, I recorded it and edited a little and here is the link:
http://www.hercodeboer.nl/mp3/Besame_sketch.mp3

Only after I recorded it I noticed that I play it in a different key than you do.
Mind you, it's just a sketch.... and my guitar isn't half as nice as yours too ;-)
I also put in a trumpet bit with some other chords.
On two points in the music you hear the bass a bit loud. I don't understand why that is (it happens when I play a DM7b5 coming from Fm7: es-f-as-c > d-f-bes-c)

Some of the chords are tricky, because of the way the PSR interprets the chords, so I sometimes had to do it in a strange way. To emphasize certain notes in the chord, one also needs pick the right style - not all styles or variation sounds alright.
I didn't write down the chords yet, but I could explain what I am doing, but it being a bit late now, I go to bed. If you are interested I'll let you know tomorrow.
drdalet