for a .243 single shot new england handi rifle what would my best bullets be for groundhogs and coyotes?

Sierra 85gr. HPBT. Can also be had in factory loaded ammo - Federal Premium loading.

That should be a good choice. Handi Rifles prefer lighter bullets as a rule. Mine shoots 80 grain bullets real well. I shot best with the cheap PMC 80 grain bullets. It would group well under an inch with those shells. If you reload, use the slowest powders that they list and keep the loads down to about 85-90 percent of MAX. Doing so will bring out the best in the NEF rifles. As a rule the Handi rifles like lighter bullets, slightly reduced loads and they don't generaly like the bullets seated out real close to the lands.
I have eight of them (SO FAR). From 223 to the 45-70 Buffalo classic.

try the 70 grain TNT

another vote for the 70gr tnt

where can i find these 70grain tnts?thanks

Leekboy,
SPEER

I would second the 85 Sierra vote! Have used this bullet for years in both the .243 and the 6MM-284. It is not only a good varmint bullet, but works very well on deer sized game. One of my companions shot a cow elk last year with this bullet in the 6MM-284 - went down in about 5 seconds from a lung shot.

Another real sleeper all-around bullet in this caliber is the 87 grain Hornady Spire Point. I never got quite as good accuracy as with the Sierra, but the terminal performance is great.