I would not recommend a night vision gen 1 to shoot a coyote from that distances, not only because the lack of illuminator power but mainly because of the short magnification (3x to 5x, max) - it will look like you are shooting rats. Plus, they cannot see the IR light but they will see the red lamp of the illuminator. You will not be stealth.
From what I’ve heard, nd-3 is, in the end, a “powerful torch with green color light”. I know it’s a laser, that can concentrate the beam of light at great distances, but it is a light. And there goes your stealth again. You will probably shoot the first ones, but after a while they will flee after you light up the nd-3.
What you need is a good 3-12x56 30mm tube scope with illuminated dot at the center of the reticle. And don’t get fooled with highly illuminated reticles because they have no use in night hunt: a good scope will allow very low illumination of the center dot only, so you can see very well your target. I have a zeiss with two reticles, a small cross in the first plane and a dot in the second plane, both illuminated, and although they both can be dimmed to very low intensity the dot is always the best choice at night.
More than 12x at night is useless if you are using only natural moonlight, as is less than 7x especially if you shoot from more than 75 yards.
A daytime scope in that configuration (3-12x56) will allow you to hunt completely stealth at night for almost 16 or 17 nights a month (starting around first quarter of the moon), as long as there is a moon in the sky (even if it is covered by clouds that allow diffuse light). And no, you don’t have to have a zeiss; a meopta in that configuration cost half of the zeiss and will let you see and shoot the same animals at the same distances. And if you want to buy similar for much less (as long as you don’t use larger calibers than 30.06 spring.) you can get a bushnell trophy 3-12x56 (illuminated) – it’s a low budget choice but very common in Europe (UK have it also).
Ps: for the other nights, without moon, get a cree led torch from ebay and shoot more close, because coyotes won’t see you as well either ;-)