Cmon guys dont anybody watch the history channel,its called HYDROLICS,the roman empires aquaduct system was built using this method,the more water forced into smaller pipes the more the pressure will increase,uphill or downhill is irrelevant.There is a formula to it somewhere ive seen on how far uphill you can go depending on current or some shit but it works & works well too.

If you do as you planned & string a line between the river banks & the current is decent you should have no problem,you may want to run 1/2 inch hose half way then reduce further down to 1/4 to keep good pressure,if its a real long run like a hundred yards just keep reducing the line till it reaches the garden.