Not every twine can be used as spring twine... like, the twine you find at Homedepot or other big box stores... Not strong enough to withstand the pressure of coil springs over great lengths of time. You must use a twine designed for that type of pressure.
Here's what I use, but I am sure there are other brands that are just as reputable if you can find them. I have even seen nylon rope used. It just must be rated for a lot of pressure. This material comes in a 1 lb or 5 lb roll. If you tie a lot of springs, go for the bigger option.