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"... I've read quite a bit on the .243 and it appears to be a good option. <> Similar trajectory, 1000 yd+ reach, cheaper reloading, less over-penetration on coyotes, less recoil = longer bench sessions...seems like a winner.
And what is barrel life like? I love my Sendero, so which Rem700 version would be a good starting point in the chambering (I would bed/do trigger as necessary).
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The 243 with a 100 gr game bullet will over penetrate a coyote - that is, it will run through a 'yote from head to tail, and keep on going, and going, and going.
The 75 and 87 grain V-Maxs would be much better choices - they are fragile and will break up. They will still leave you with a mess, but won't travel into the next county to make another mes (legal and otherwise).
Coyotes, even the large ones up in the Connecticut/Vermont area of New England, don't need that much killin'.
For rifles that are similar to your Sendero, you have a problem. Remington makes a fairly large line up of varmint rifles with stocks that are similar or identical to the Sendero, but not in 243.
In 243, they only make one, and it's in a laminated wood stock.
Barrel life will be in the 1,500 range if you want accuracy to still hit 'yotes way out there.
If you are willing to consider cartridges other than the 243, then there are Remingtons that are a match to your Sendero.
There was a time when every model of varmint rifle was chambered in 243, but that is not the case any more - more varmint shooters are going back to the .22-250 and the .220 Swift for long range varminting.
Both of these would also serve you well to 600yds.
For 1,000 yds on a 'yote, you will probably have to go with something further up the ladder, like a 40XB, or a custom rifle.
1,000+ yds is a fur piece on a dog sized target!