What does "small amount of ease" mean?

If you say you want something to occur with a "small amount of ease", what are you actually saying? I understand that the intention of this phrase is typically that you want something to be done easily; but, does it literally mean that something should be hard?

It's a meaning of ease rather specific to sewing (or clothing): “space to move within your clothing”. So, “a small amount of ease” is synonymous with “a little leeway”, “a margin of safety”. It does not mean “effortless”.

Google Books provides some real-world hits of literal use of this expression, though it appears to be used figuratively in your case.

No native English speaker would ever use small amount of ease to mean effortless. The only context I could imagine it being appropriately used is if you were applying ease to something with the intent of loosening or lessening pressure, e.g., altering a garment or fitting a pipe.