Cursory googling suggests that from an 11.5 barrel, 55gr V-MAXwill have a muzzle velocity of around 2550 fps.
Hornady claims that their 55gr V-MAX expands down to 1600 fps, for reference.
For those of us who like math, this combined with a stated .255 G1 BC gives us the following.
1800 fps to 240yds with 10 inches of drop.
1700 fps to 275yds with 16.5 inches of drop.
1600 fps to 315yds with 23 inches of drop.
An
existing post regarding 11.5 with a SOCOM RC lists 2930 for the BH 50gr TSX load with a SOCOM RC can. With a stated .197 G1 BC, that's
1800 fps to 265yds with 10.5 inches of drop.
1700 fps to 295yds with 15.5 inches of drop.
1600 fps to 325yds with 22.5 inches of drop.
I would suggest running the 50gr TSX, as the higher velocity (likely due to faster burning powder) means a flatter trajectory. You could also benefit from tweaking your zero to maximize the point blank range.
Here is 55gr V-MAX vs 50gr TSX with 200yd zeroes.
To answer your question with this rough math, an 11.5 with a fast bullet is certainly sufficient with regards to lethality. How much drop matters is up to you to decide. The 55gr TSX loading is a bit sub-optimal, but I have three numbers so it's a decent example.
200yd Zero 55gr TSX comparison. Going off of the fact that 50gr TSX is substantially faster at the muzzle, you'd probably be just fine with an 11.5 or 12.5 weapon.
The above is all citing other people's numbers and is somewhat limited by the dearth of data for 50gr TSX, which I suspect is your winner. Thus, I'm going to go ahead and construct a sloppy data fit to estimate 12.5 and 13.7 velocities for you, using the found 10.5, 11.5, and 20" velocities. I must emphasize that these are estimates.
Using the following data as reference -
0 0
10.5 2750
11.5 2930
14.5 3250
20 3419
Produces the following trendline.
From this, we derive our 12.5 and 13.7 velocities of
3046 fps
and
3179 fps
respectively, leading to the
following set of trajectories with 200yd zeroes. I must reiterate - this is an approximation on my part, but one I am fairly comfortable making.
Tl;dr - 50gr TSX or 55gr V-MAX will expand in a coyote out to 300yds with whatever you choose. Go longer if you need to to get better drop and more margin for error. Buy 50gr TSX.