Welcome to GoY, Debbie!
What you plant in front of your fence will depend on whether your border will be in sun or in shade. Also, where you are in country will influence the choices. For example, up here in the cold north, lots of plants will not thrive or even survive over winter.
I am sure you were hoping for a more helpful answer, but there will be lots of help once we know more. I promise.

do you mean that all the plants need to be black-- this is probably possible even if in name only

I'm not at all sure what Debbie means here - either its black planting, or more likely, some kind of black coloured edging along a border, not plants. Which is it? Although I'd never put an edging on a border anyway unless it was essential...

Ornamental grasses come to mind such as 'Black Mondo grass' it is an evergreen perennial with shiny foliage making small slow spreading clumps with white flowers. It is full hardy and like any soil type. there are quite a few black plants which may be black in foliage and or flowers such as the black Iris 'Before the storm'.
There is also a book called 'Black plants' by Paul Bonine which lists 75 which include "Black" Hellebore and 'Black Parrot' Tulip
You can add a black slate or very dark bark mulch and quite a few modern containers can be found in black.

Agree with Bamboo question, as it stands, is not answerable.

I'm not sure its not been subtly altered, MG - it seems to suggest its planting that's required much more clearly now, but maybe it's just me. I can't think of anything which will be tall and narrow which is black anyway. Well, apart from black bamboo, and that looks green unless you look closely anyway.

I can think of several plants/bulbs that have 'black' flowers but the whole plant black - don't think such exists, couldn't work for photosynthesis. There are various Sambucus' but again it is only the leaves that are a purply/black...

Hmm, well another question's been posted saying its an edging, not black plants, folks...

Yup spotted that!