I assume you are out of a vehicle with this setup.
The SureFire M4 will allow you to see a coyote out at 200 on a clear night without a red filter.
The M4 comes standard with two lamps, 250 and 350 lumens respectively. You can get a 500 lumen lamp separately, originally designed for the 12PM/ZM. It is/was the MN62. Due to the power draw required for this lamp, the batteries will go into thermal shutdown after a few minutes (5-6). When they cool down, the light will function again.
There is a red filter for the light, the FM25. I believe the aforementioned FM24 is a beamshaper.
You may be able to still pick up eyes only with a filter on. But runtime will be an issue in search mode.
An SureFire M3 Combatlight with a Turbo Head is your next option. It will still reach out there, but not quite as far.
In a vehicle makes you life easier. Get a K-Mart cheapo spotlight. They work quite well for finding eyes with a red-filter on. When it is time to shoot, have a partner take the red filter off, get yourself situated. White light on at last location, pick the target up in the optic, shoot between the running lights.
Not that I would know or ever did this on BLM controlled property.
If you really want to see and get into the HID realm, consider the McCullouch X990. Reasonably priced for this class of light compared to the MaxiBeam, really throws a large quantity of light out there. Focusable spot to flood, 2 NiCd batteries and a car adapter.