Another vote for the Simmons 4x32 ProDiamond. Simple fixed 4x scope that is durable with decent glass and good eye relief. I've used mine on a TC Omega for 5+ years shooting pretty stout loads (120gr BH209 with either 350gr FPBs or 240gr Speer DCHPs) with no problems. Natchez should still have them for around $60.
Re the 4-16x40 CenterPoint, I would stay away from high magnification bargain scopes. Your money is much better spent with a lower mag fixed power scope with decent optics and with a muzzleloader, you do not really need the extra magnification anyway.
If you are not comfortable with the 4x power, the Cabelas Powderhorn at 3-10x40 is available
here for $49. A great deal on a good scope. Cabelas backs up their products without question, don't know whether Wally World's CenterPoint will.