Too much modifying, most likely.
I suggest you spend a lot of time digesting this thread first:
http://teamswift.net/viewtopic.php?f=10&t=54584It says it is about Koni damper options, but it also describes the critical dimensions of stroke and overall length and addresses what you need to do to make a coilover work at the top of the strut.
If you can figure out what the stroke and length are on the Neon and they are miraculously the same or a bit shorter, then you might think about cutting off the tabs that fit the knuckle and welding on the Swift tabs. That's on the front. Forget the back.
But if the dimensions were close, Swift guys would have done this years ago--your real options are pretty much covered in the link.
Some bonus information: getting coilovers right on a car with macpherson struts is not straightforward. The setups you can get on ebay for Honda's double wishbone suspension do not work on a strut and anything cheap is likely dangerous.
If you really want to lower your car and improve spring rates on the cheap, see the section on cutting springs.
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http://www.teamswift.net/viewtopic.php?f=17&t=57216