This was frustrating for me for a while too. Especially because I use Media Center on the Mac and the answer to my problem wasn't quite as easy. Here's the deal:
Play/Pause with spacebar is implemented by default, as you have seen. However, if you are clicked into any area of the interface that can use spacebar for some other function, it overrides this and uses the spacebar for other things. Like in the Navigation area, spacebar expands and contracts tree views. I have ZERO reason to use the spacebar for navigation, even though I love keyboard shortcuts. Frankly, I think it's rather backwards that JRiver does this. It's backwards from every other player on the planet.
So I've remapped spacebar to override almost every function it has in MC and replace it with Play/Pause. I've kept the ability to type a space into entry fields like search, Tags, etc. So my spacebar doesn't do navigation, or any other "special" functions. It just does Play/Pause (almost everywhere) and types a literal space character in key entry fields. This is perfect for my needs. If you want to do this yourself, here's how:
You need to copy a template file into a Custom Resources directory so JRiver can read it and then read your keyboard mappings from it. See here for a template and the location to copy it to:
http://wiki.jriver.com/index.php/User_Defined_Global_Keyboard_ShortcutsOnce you've done that, go to the bottom of the file and find the Accelerators section. I like putting my keyboard mappings at the bottom of that section (on a line before the </Accelerators> marker). Here's my keyboard mapping for space bar:
<!-- Play/Pause -->
<Entry Key="Space" Command="10000" Param="0" TranslateFlags="21" />
It's kind of a medium high amount of effort just to map one key. But for me, it was totally worth it. Hopefully I've saved you about 90% of the research I had to do to figure it out.
Good luck!
Brian.