This app was mentioned in 2 comments, with an average of 2.00 upvotes
Looks like AnySoftKeyboard with the Esperanto pack is what you're wanting. It doesn't have a Swype type deal, but it is suggesting words to me as I type. It auto-corrects in some cases, though all my Esperanto words are showing up with a red-underline.
If you're on an Android device I'm sure there are a few keyboard solutions.
https://play.google.com/store/apps/details?id=com.anysoftkeyboard.languagepack.esperanto&hl=en