"A palm-sized piece of land" sounds a little strange, I think. I am trying to come up with comparison words but none spring to mind (perhaps someone else will be able to do better - sorry).
I think it would be best to make a comparison with something actually related to land. How small do you mean, exactly? For example, you could use:
(1) "A land the size of a vegetable patch"
(2) "A vegetable patch-sized plot"
(3) "An area no larger than a humble household garden"
Oh! You could use "Lilliputian" - as in "a piece of land of Lilliputian proportions" - but it really depends in what context. If it's some sort of report (e.g. survey) I wouldn't recommend it as it would sound a bit too arty and not scientific enough.
The word comes from a very well known book by Jonathan Swift, called Gulliver's Travels. (I can't post links yet but look it up on Wikipedia or something for more information) Anyway basically in the book the protagonist, Gulliver, travels to a land called Lilliput where everything is of miniature proportions.
A small patch of land/the size of a vegetable patch/a garden the size of a pocket handkerchief/the size of a postage stamp are some of the many descriptions I have seen used to describe a small plot/piece of land.