You don't need a linux machine ! I've said about 5 times lol
Partition your drive using whatever OS you like. Just make sure you have two partitions. The first needs to be at least 1G the second can be as large or as small as you like.
How do you partition a USB flash drive? Windows 7 doesn't seem to allow that.
I can't get persistence working with unetbootin.
You should be able to, but not with the simple format tool, that just formats partitions. Using gparted on linux is easier. Make a 700MB vfat/fat32 partition for LinuxCoin to be installed to, then format the rest as ext2/3/4 and name it "live-rw". You won't be able to format that with Windows anyway...
To partition in Windows you have to open up the hard disk manager and do it there. But you still won't be able to format as a Linux filesystem. And as greenlander said, you can just use a second drive as the persistent drive, just label it as "live-rw".