Is it an easy option to ad a timing chain tensioner to my Mk2 Cooper S?

What are the requirements and/or modifications?

Not commonly done.
I did it once on an S motor that had a loose chain, because the block had been line bored. That had shortened the sprocket centres. That also retarded the valve timing.
You need:
A+ timing chain cover and gasket.
A+ engine front plate.
A+ single row tensioner assembly. Duplex one is NLA for many years.
Single row one works.
Offset cam key. I needed a 9deg one. You may not but check valve timing on assembly.

I built this motor 20+ years ago for a friend and it is still running fine.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

Guess I need an offset cam key to take the slack out of the chain.

That won't take the slack out. What chain is it, many are Asian rubbish now.
Iwis German made endless is the best. Not cheap but worth it.
You shouldn't need a tensioner unless block has been line bored since manufactured.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

The offset woodruff key is to adjust the cam timing vs the crank. It won’t affect the tension, as the Dr says

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If the engine has been line bored then wouldn't the main bearings be larger than standard bearings?

When you line bore the block, you remove material from the main caps, then rebore while taking as little material off the block as possible. You essentially just move the bearing surface towards the top of the block while maintaining the bearing bore diameter

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So if your engine has been line bored the timing chain is going to have some slack?

Yes. With standard sprockets and chain.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

And keeping in mind that generally you only need to line bore the block if a main cap is missing or damaged or the bearing tunnel is damaged from a spun bearing.

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Is there any difference between a Cooper S chain cover and a Mini chain cover? I ask because the chain is duplex.

Some Mini timing covers have a metal reinforcing across the centre. Cut it away if fitting a duplex chain.
Also note the oil slinger for duplex chain is narrower than other Mini ones.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

Rollmaster make duplex timing gear sets for line bored blocks that negate the need for A+ tensioner set-up. Have +0.002" and +0.005" new sets available.

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Steve

What is the Mk2 oil slinger part number?

I believe this is it but others can confirm - 12A1148. Available from most Mini parts suppliers.

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ex-NSW Police 1970 MK II Cooper S
VMCI #43