Supposedly if you drive a copper nail (I think)into the trunk of any tree it will eventually kill it. Or just cut the tree down and hack up the main root which will in turn kill off the rest of the roots.
Bear in mind these trees grown darned high and their roots will go a long way underground - hence so many drainage problems are caused by tree roots damaging the pipes, and subsidence to houses because of tree roots damaging the foundations.
With a few exceptions cutting them down will kill them, they won't regenerate from old wood. If you have a specific tree in mind post the name of it and someone can tell you
I'm afraid the copper nail won't work, even if it did the last thing you want is a large dead tree threatening you
Copper nails - only if you have several years. Employ a recognised tree felling contractor. You are likely to need a licence from the local authority - check first.
I just wanted to add that Conifers actually have a rather shallow root system unlike deciduous trees (oak, elm etc). This is why you find them in the colder climates where deep rooted trees cannot/rarely do, survive due to the under ground permafrost which the trees roots cannot penetrate.
If it's next doors trees, dig chalk into the ground on your side of the fence.Wait 3 months and they will be nice and brown. (conifers need acidic soil. Chalk will neutralize the soil. YES IT WILL WORK!)