I think you have a plan there Accy. Presumably you want to sun it so that it can grow faster and not develop a tan?
Anyone who suggests that you spraytan it is of course just silly, we all know it turns stuff orange, not deep green.
I have been thinking about his and I have some suggestions. I hope they are useful.
1) Ask the sunbed salon to turn the bed upright. That way you don't have to lay your palm down. Put the pot on a rotating platform and wind some string around it. That way you can remotely pull on the string and the pot would rotate, giving the plant (what his name, BTW?) an nice even exposure on all sides and you can remain safely behind a screen or such and avoid over-exposure yourself.
2) Then, you hint that it is growth, not colour you are after. Growth comes from photosynthesis which converts carbon dioxide into starches. In other words, you need to introduce some CO2 into the booth. I think a nice large block of dry ice would do the trick. With all that CO2 in the booth, the string trick is another reason why you don't want to be close to him whilst he photosynthesizes.
3) Plants also need nitrogen to stay green. In nature this is supplied by lightning - yes it is true - and it makes its way into the soil that way. You need a lightning generator of sorts in there too but I cannot for the life of me think how to do it. I'm sure there will be many good suggestions forthcoming.