To suggest solutions, we need more info, please.

First: Do you know the source of the water? And roughly where in the US are you? Is the water there because you are in a very rainy area? Or is there some other cause for the constant wet spot?

Second: How large is the problem? Is it a five foot puddle, or is a larger part of the adjoining yard also overwet?

Third: How long have you been in the house? Is this just an early spring problem, or does it stay that way across seasons?

There are a number of things that can help, but we need to get more info on what is happening.

How about putting some pieces of slate there as a stepping-place?

I suspect that plain concrete slabs will be your best bet, as they won't break the bank and are easily reversible if you decide on another approach later on. Any big box store will have them in probably several sizes. My personal favourite is 24x24 as you can lay out a nice-width pathway or small patio with just a few, but they are &*(% heavy so you might prefer 18x18. Anything smaller and I think you'd have stability problems with them though if it's not really mushy, even 12x12 might work. If you're in a zone where it freezes while you have standing water you will get frost heave, but you might just be able to relevel them every year - the alternative is to dig down and put a proper base, which kind of loses you the "fast and cheap" advantage that these slabs offer.

If you prefer natural stone to concrete, you can also get cut or hand-hewn natural stone slabs, bluestone or what have you.

You're likely best off with a textured surface in case it gets slimy and thus slippery. That's why a wood surface there would not be advisable.

KarinL

I would suggest you determine why there is a puddle there. Is the bottom of the stairs at the base of a slope that recieves and/or channels run-off? The other item to consider is where will the water go once it's displaced from the current puddle?

Others have already given you good advice about looking for a drainage problem that may need correcting as the first step. On the other hand, if it is not due to water pooling there with no where to drain off, but simply that it stays damp after rains because it is shaded, then adding some hard paving stones/pavers/flagstone, etc in this area can bridge the wet spot giving the access to the sunnier/drier portions of the yard. You might also consider adding an at grade level deck as an extension of the last step to extend out into the yard. This could be as simple as using sleepers of pressure treated lumber over concrete post bases, and low plantings of ferns or shade tolerant shrubs could be added at either side to make it look more "nested".