I would be cautious of trying to change the colour of your bench, inevitably the colourant will fade and possibly even flake off in patches. If you decide to go ahead you will need to use primer and then the actual paint.

Hi if its only been coated in linseed oil (no varnish)i would first go over the bench with white spirit ,if you havent found a suitable paint i generally use Sikkens Cetol HLS or maybe you could find the equivalent online.If you can still see the grain of the hardwood through the brown ,this type of paint will enhance the grain and will still have a green colour.The green colour i use is green hindelopen.Which is a satin basecoat and wood stain.Hope this helps:)))

Cuprinol do tins of garden furniture protector and furniture restorer, some G C,s have a range of colours and may be able to advise you

I have just painted our trellis with Cuprinol Thyme a lovely shade of pale green and my wheelbarrow it Iris blue.

I will post photos later .

But we would not use this paint for our table and bench.

As its water based paint but ok for what I need to use it for.

Got the paint in BQ

Thanks for your replies. I didn't want to chance a mistake, so have opted for Rustin's Danish Oil. Applied it with a rag, and it was an easy job to do, so still brown, but fairly sure it will cope with the weather.
Scotkat, my limited knowledge tells me that a water based paint simply won't stick to an oil, so Cuprinol Wild Thyme is going onto my new fence, (when it stops raining)!