If you're looking for an updated OS, you should contact the device manufacturer and ask them about it. Generally for cheap tablets the installed stock ROM is all you ever get.
Your best bet is to root and unlock your tablet and install a ROM that has Google Apps available for it. Since you don't list your tablet model, that's the most specific advice on that score I can give.
Failing that, there are lots of third party sites around that you let download the APKs (installation files) for apps independently of the market place. You can install them so long as you have
Unknown Sources checked in
Settings->Applications You can either visit those sites directly on your tablet or visit them on your PC and transfer the download APKs to your tablet via your home network. You should be able to install them just by navigating to them in a file explorer and clicking on them ("sideloading"). I like Android Community myself.
Caution: you run a much higher risk of getting malware installed on your device this way. I would advise installing an anti-malware app like Prey on your device.