Engine is a 31R707-0001-G1.   Had to replace the compression release cog.  Put everything back together, set the valves.   Getting a low throttle knocking sound which was probably there prior.  It isn't at the rocker arms.  No bent rods.    Seems like there is some play at the piston arm (lower) and the counter balancer arms seems like they have a little play as well.   How bad of a job is it to replace the piston arm?  And for the time and parts cost is it more effective to just replace the engine?

https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/briggs-stratton-engine/200000-399999-series/31r700-to-31r799/31r707-0001-g1/air-cleaner-blower-housing-trim-rng-exhaust-system-flywheel 
 
The part you refer to is the connecting rod.  
 
To access and change involves pulling the head, side cover and the two connecting rod bolts.
I beileve you have a balancer that lekely needs removal (a lil tricky, but do able).
 
If there's aluminum (from the rod), onto the crank, it can often be removed with muratic acid and careful polishing.  There's numerous video's on YT showing it. The crankshaft (and flywheel) would need removal.
 
Re parts,-connecting rod, side cover gasket, head gasket, valve cover gasket and I believe that'll do it.
 
Look up the parts on the link I provided for the parts and prices.  If you can feel that rod have movement (more than approx .003"), it NEEDS attention.  If not repaired, the engine will eventually 
literally blow up putting the rod thru the block (now a parts machine).
 
.
 

Appreciate the reply.   When you move the rod side to side it has quite a bit of play.   I'm not 100 sure the counterbalance arms are sound.  I can do it but when I add up the parts cost, my labor and just the time it would take to get everything off and then back on - I've seen new replacement engines that are in the low sixes.  I'm a little concerned that when I put in new oil, ran it for a few minutes and looked at the oil - it is VERY dark grey and looks like aluminum may be in the oil.   It immediately shouldn't be this dirty.   I used to use a service and bought this mower for 300.   It's paid for itself many times over.  My service charged 1950 per year.  If I get another three years out of the machine with a new engine it makes sense.    If I had the time this winter maybe the rebuild would be an option.  I just don't want to go through the part expense and time, put everything together and still have a problem especially if the piston and cylinder aren't perfect.   The last owner I don't think did a good job maintaining this mower.  He had a perpetual leak at the valve cover and maybe the main seal.   More than likely the engine's oil at some point was low and he still ran it.   

Well, you can tear it down for free and see if you can find the issue.
 
Some back and forth play on the rod is normal, up and down on the crank, no.
That balancer is steel on aluminum (from my Toro 18 HP mower);