Hi....
Sorry for getting back so late, I just got home from work, been a crazy day....
Actually, java moss in most cases will grow very slow. That is the reason why algae becomes attracted to it so easily, as the moss sometimes has a hard time competing for the nutrients.
Another thing is the lighting. Java moss is a low light plant. And it will grow slow in low light. Another reason for algae. But if you upped it to the lower end of medium light, it will usually grow a bit faster. Mine now grows quite fast, and quite well. The trick is in the eliminating of any algae, and lighting and nutrients.
I will give you kind of a run down on my particular tank, which you might be able to use bits and pieces to make yours work.
My lighting, I'm running a 65W 50/50 CF bulb on the tank. So I have only about 32.5W of usable light, putting me at around 1.25w/g. The other 32.5W is actinic, which only helps how the fish look.
When I had algae, I dipped the java moss in a 10:1 solution of water and Excel, and let it soak for about 3 minutes, then place directly into the tank without rinsing. This got rid of the algae, and the moss had a nice spurt of growth as well, algae free. I also dosed Excel for a few months after that to keep things looking good.
Currently I don't dose Excel anymore, and it's staying algae free. I don't even get spot algae on the glass.
Another factor that helps is new bulbs. Old bulbs tend to shift from the more blue spectrum to red, which is the main cause of algae from older bulbs. It's not near as bad with CF bulbs because they hold the spectrum much better than regular florescents, but I do change my bulbs when I feel it's needed. For the CF's, I run them about 18 months before changing. Regular florescents I change about every 9 months.
Lastly, nutrients. I do not dose nitrates or phosphates, as I have a heavy fish load, 28 fish in a 26G tank. But I do dose Potassium once a week.
As for growth rate, mine doubles in size about every 3-4 months.
Here's the link for Flourish Excel.
http://www.bigalsonline.com/BigAlsUS/ctl3684/cp18480/si1380246/cl0/seachemflourishexcel500ml
Hope this helps. Any other questions, feel free to ask. I'd be more than happy to help.