macOS Sierra is compatible with all Macs (MBP, MBA, Mac Pro, Mac Mini and iMacs) 2010 models and later, and MacBooks starting with late 2009 models and later. Here's a reference.
Otherwise, to boost the performance of your Mac, you can in theory double the RAM to 4GB (EDIT: your model seems to support a max od 2GB RAM, see my comments) and may be swap the HDD with an SSD (not sure about compatibility of your old model with SSDs - someone else might chime in).
I am a strong advocate of repairing, and reusing and extending the life of your device (indeed my computers date back to 2012 although I have every opportunity to upgrade since I trade new and used Mac laptops), but in some cases you just need to move on. This is one of them. The only way you are going to make you 11-years old computer go fast again is strap it to a skateboard and push it down a steep hill.
And no, unfortunately you're not gonna find a new computer that's going to last you as long the one you're currently using - in my opinion.