The IEEE output style works for me in that no space is generated between the citation’s closed right bracket and the cursor (see attached image; yellow highlight shows the cursor’s location).
You might check the citation templates* to see if a blank space was mistakenly added at the end and just delete it. Or download and install a new IEEE output style from .http://endnote.com/downloads/styles
*Go to the EndNote toolbar, select Edit > Output Styles > Edit IEEE. Locate the Citations section then click Templates.
I guess you mean in the bibliography not in the citation in the text? Where are the instructions that you are following? It would seem to be pretty ugly to have no space between the bracket and the Bibliographic reference itself? Most times one prefers a tab or space?