Is there a website or tool that will allow me to choose a group of equally separated list of 10 colours from pastel green to pastel red to be used as the background colour in the cells of a table?
Did you come across this site in your Googling: http://www.colorhexa.com? It has the ability to generate gradients between two colours, but it generates them in 12 steps rather than 10. If you fiddle around with your colours, you might be able to get the colours right.
I also found this website: http://www.perbang.dk/rgbgradient/, which has less features than the other one, but you can specify the number of steps in your gradient.
You can use Adobe Illustrator and it's Blend feature for this. I don't know if you have Illustrator available, but I do this all the time for color transitions.
Object > Expand Appearance and you'll have 10 objects ranging in color from green to red. Simply sample those colors or add them to the Swatch Panel and save as
.ase for other Adobe apps.