Chansey can be caught anytime. You should usually go to Route 210 or Route 209 to get it. Very rarely, it will be holding a lucky egg, which doubles Exp. from battles.
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You cant catch a happiny you have to breed a Chansey while the Chansey is holding a luck incense.
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you need to find a Pokemon with sweet scent then go to safari zone go to last grass before you can get the surf then use it find a chansey if you find chansey when using sweet scent try catch easily
The item Lucky Egg, that doubles the Exp.Points earned in battle, can be obtained by catching a Chansey in the Safari Zone. You will have to be lucky though, since there is not really that high percentage of getting a lucky egg with the Chansey you catch (and it is not easy to meet a chansey, nor catch it, either...). As a sidenote, I actually got lucky as hell and receive a lucky egg on the third Chansey I ever caught in Firered. If I forgot to mention it, the Chansey will be HOLDING the item, in case you are lucky enought to catch a chansey with it.
Since you can't catch chansey you need to trade one from firered, leafgreen or Pokemon xd gale of darkness.