Hi Jon,
Believe it or not, I get the black background by placing a potted plant so that the bloom is in right at the edge in sunlight but the rest of the plant is in total shade and the entire background showing on the screen is dark. I usually take my pictures early in the morning and our roof creates this large area of shade in my back yard that, of course, gets smaller and smaller as the morning progresses. I discovered this quite by accident, and it really works to make blooms seem even brighter and it hides the lawn area right behind it. But I think you would need a potted daylily to control where you could get the best effects, unless you could paint something black and use that as your background instead.
I have almost everything I make crosses with in one-, two- or three-gallon pots because it gets so hot and dry here in Bakersfield that I have to put plants I'm pollinating on my covered back porch for a few days and hope the crosses take, and even then most of them don't take. So I'm used to potting up everything I get now, and then it's pretty easy to get pictures with a dark background.
Hope this helps, and thanks for asking!
Betty
That is one beautiful Daylily and the dark background really makes that bloom pop! I remember talking to a couple of ladies about their photos of African Violets a few years ago; one used a square of black fabric behind her plants and another said she used a black posterboard for the same purpose. A dark background really does make the bloom the center of attention. I should take the hint and do this when I'm photographing my blooms. 
I will try this next spring when my daylilies bloom.