I seem to have a Stevens 32-40 rifle that is rather unique in its acceptance of loads.  It has an aversion for bullets in the 200 grain weight range obstinately refusing to shoot them accurately.

It seems to do its best with bullets in the 160 to 180 grain range and even seems to do best with the lighter end of those weights.

When I started with this rifle I tried the traditional target loads with powders like 4227 which seemed to be the most recommended powder for traditional target loads.  Sadly and to my surprise and disappointment my rifle turned its nose up at 4227 and similar burn rates.
Another issue with my rifle was bullet alloy hardness. It seems the most recommended alloy is 20/1 lead to tin at BHN-10 but again this rifle had a mind of its own and started to show a preference for harder alloy at BHN-15.
It was not until just recently that I decided to go in a different direction in search of powders so started trying progressively faster burn rates until I get to some of the very fastest on the burn rate chart. 
This rifle showed a distinct liking for What used to be           
IMR Hi-score  700X but is now sold under the Hodgdon label. With that very fast powder it perked right up and started shooting very respectable groups with the Saeco 170gn tapered design in fixed ammo seated with two lube grooves out of the case.
The rifle likes 700X but I do not because it binds in my RCBS powder measurer really bad.  A charge weight of 6.8 grain of 700 X got my attention so I began to look at other powders with similar burn rate that may meter more smoothly from my powder drop.
Two other powders that shot well are Alliant American Select at 5.8 grain and what I think may become my favorite Winchester WST at 4.7 grain.  The Winchester powder meters like the hopper is empty with no binding what so ever.  The American Select has an occasional hiccup but no real binding as with the 700 X.
This rifle previously gave me so much grief trying to find an acceptably accurate load that I had considered a new barrel or a re-bore because even though at best its condition is " not too bad "  I still felt that it should still shoot reasonable well for a well worn old original rifle but to that end success eluded me.

Now that the rifle has spoken and I am finally listening I am quite pleased with our merging of minds to come to an acceptable level of performance to our mutual liking. 
Lesson learned, didn't need a new barrel just needed to listen to DR. Gun   

That is an interesting idea Mike.  Sounds like maybe you have had a visit with DR. Gun too.

I think one reason I was having trouble finding good accuracy is that my original bore is less than perfect. It shows considerable ware and has a short rough section on one side about four inches ahead of the chamber. I believe that to be why it does better with harder alloy.
For the same reason the less than perfect bore I hesitate to use black powder because unless I wipe between shots it will exaggerate that problem.  I am kind of afraid that with so much wiping it will accelerate bore ware.
With these extremely light loads it is shooting good to 100 yards and for this rifle is all I will ask of it. Its just for fun shooting and with these loads it will shoot continuously all day long without wiping and consistently crowd most of its shot into about an inch at 100 yards.  I have noticed how critical the rest becomes with such a low velocity load. Any change in the location of where the barrel is rested in its length as well as support of the butt shows up on target.   
This rifle will never be a competition rifle but it is still fun to shoot it as it was originally made and have it shoot reasonably well for someone not having high expectations.  I like it too with the light loads because our nearest neighbors maybe a little over a quarter mile away  may not even hear it.

Marlinguy
That sounds like very good advice to me.  For these vintage BP rifles and cartridges 1300 fps seems like magic.

I may have found " THE LOAD " for the 32-40 today. I tweaked a couple things with the 8.5gn 2400 load. One was to drop lube from three grooves to two of the five on that Saeco bullet. Another slight change was to seat the bullet one drive band farther out and add a firm crimp at the middle lube groove. I also went to fired but unsized cases and upped the bullet diameter from .321" to .323". The last groups fired for the day today before it got just too hot out were maybe the best the rifle has ever done for me.
Oh yea and another thing the bullets I thought were BHN-15 tested today at BHN-22. They tested BHN-15 about 24 hours after casting and quench cooling them but now about a week later they are testing BHN-22. The same alloy air cooled tested about BHN-9.5

It looks like your rifle and mine may like similar loads. I have a 7 groove 32-40 Darr with a 1:16 twist. The bullets in the 200gr range are just tipping a hair when they go through paper at 200. I have been using a flat nose Paul Jones 180 with ramshot enforcer (around 12.2 GR) with great success. Enforcer seems to be right at the 2400 burn rate, might be interesting to try

I have not chronoed it yet to see what kind of spread I am getting, but this weekend we had our 100yd match and had a score for group. We did 2 - 5 shot groups and I managed a .696 and .670. I started testing at 12 GR and worked my way up to somewhere around 12.5 for my sweet spot. No wad, but I am tempted to try one.

No complaints yet, too damn bad I can't get that group in the 25 ring!