coaster brake and chain tensioner

Yup.
And nope.

One cannot use a typical tension device like a multi-speed deraileur.
If you can use a motorized bike drive chain type of tensioner and keep the overall chain deflection down to an inch or less, you should be fine. Just remember the side of the chain that has the load on it will go tight and the opposite side loose.

Pedal power = top run tight and bottom run loose.
Braking power = top run loose and bottom run tight.
 
As always GearNut is correct. I run a chain tensioner on my pedal side chain on a coaster brake hub. The tensioner is fixed, adjustable but not spring loaded therefore the chain is always the same tension when pedaling or braking. Never had a problem with this setup.
Granted, the tensioner bracket must be rigid enough to prevent any flex or loosening of the chain when braking but if designed right that's not a problem.

Tom
 
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like they said...

pedaling backwards when braking creates an enormous amount of force, a lot more than you'd expect, and any cheap tensioner would fail.
 
I made a spring loaded one for my bike...

But it’s designed so the end of the tensioners travel slightly exceeds the the taunt chain while the brake is being used.

-Kirk
 

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