A year or so ago, I had an email exchange with Kevin from Straight Shooters regarding .20 Diana 34s. It seems they bought a few, but couldn't get them to shoot worth a $hit. He said the bores were oversized, and they had a dickens of a time finding a pellet that would fit and shoot decently. They opted to not even sell them.
Personally, I'd love to have a 34 in .20. I have a 34N in .177, which is just about the most accurate spring gun I have at long distances. I've been a fan of .20 ever since I bought my first air gun, a Sheridan H pistol. A .20 34 would be ideal in my mind, but alas, they don't seem to be good shooters.
Again, this is second-hand info that I got from Kevin at Straight Shooters. Send him an email for the straight poop.
It seems that there is little choice in .20 cal. ammo, which limits the probabilities of testing and choosing the right pellet for a .20 cal. airgun. I was recently inquiring re a D54 Air King in .20. These were available a year and a half ago but as the only pellets available were those made for the Sheridan (5.0 mm) in the yellow box, that are not waisted, they didn't shoot as expected and now the .20 cal. Diana 54 is History.
I have a model 48 in .20 cal. It is the best air rifle I've every owned. Barrel fit is great - nearly any .20 cal pellet I try fits snugly. Way better than they do in my R1 Beeman. Way better. It also outshoots the Beeman by a wide margin. Great gun and .20 cal is the way to go in my opinion.
Don't know how similar the Model 34 barrel would be, but mine is fantastic.