Or you could get a Wingbo, coddie! Someone on here (will search in a min) bought one by accident () from a German on Ebay and didn't really know what it was, empty it looks like a giant baby catapult (wheeeeeeeee!) but you put the babe in it face down to swing a bit, and when they are a bit bigger they can swing themselves I think.
Here it is, it was adell - there are links to a couple of pics.
This is wingbo's home page in English. It only lists retailers though - all in Germany - no internet ordering apparently - but you could email and ask about mail order if you wanted. They look very cute! (But Twinkie's wind-up swing idea is probably better.)