We need your geographical location (state, large city) to be able to make plant suggestions. And I assume you mean something permanent when you refer to 'perennials' rather than the "die back to the ground in winter" nature of herbaceous perennials.

Apologies, it's Michigan, outside of Detroit. Location is typically a wet location.

Wet as in persistently soggy or occasionally wet/damp? And how tall would you like this plant to get?

In the spring and fall it typically remains soggy. I would say no taller than the post itself, so a couple feet. I don't mind pruning/trimming if necessary though.

Hard to find a permanent or woody plant that will stay quite that small. But that would be my preference over something that will disappear for 6 months of the year. A few that would be under consideration are Clethra 'Sixteen Candles', dwarf Fothergilla 'Blue Mist', Cornus sericea, Salix purpurea 'Nana' or Salix integra 'Hakuro Nishiki' and Itea virginica 'Little Henry'

The cornus and both salix will need pruning to keep the size in check but that is also something that is done as a matter of course with these shrubs.

Add more soil to raise the level. How about a bush like forsythia? Plant three feet from fence.

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We have always liked the yellow color of a forsythia, but don't most grow to be quite large? What would be a good compliment to a forsythia if we were to plant just one for each fence?

There are dwarf or compact cultivars of forsythia that could work. But while a bright and cheery yellow for a few weeks in early spring, it is a green blob for the rest of the season........any fall color is iffy at best. I'd want to consider something that had a longer season of interest.

And you would have to fix the wet or soggy conditions to accommodate the forsythia. They require good drainage.