If you're on Android, you can try the mobacoin offers for trying out their other games. You can get up to ~700-800 coins that way, before the flow dries up.
If there are other shady ways, like coin generators, it is illegal and we will not talk about those here. I think the mods will ban anyone who does. To me, it is the same as forging money. And forging money is basically robbing everyone else holding that currency (because it devalues that currency slightly - Economics 101).
Those mobacoin offers are all bullshit, I triend once with many games downloading and didn't get a single coin, and later I get a message where they apologise for a failed attempt to redeem code. And they want me to try again. How can I try again, if I already downloaded and registered it?
The Mobage run "free coins if you download our games" offers are the only constant, and safe, method. There are occasional promotional give-aways, usually tied to their Facebook page, but can be tricky to actually get the payout on those.
Be cautious of third party sites. Not saying the sites listed in this threads are bad, never checked them myself. Merely saying that, like most things on the Net, they may offer you candy... but there might be a windowless van around the corner. Annoying as hell to get some of those spyware/viruses off a computer, just for 100 mobage coins. Use your best judgement.