I just bought a Hopkins & Allen falling block and a Remington rolling block in 32 rimfire. Both anre substantial robust actions that would hold more powerful cartridges like 32 S&W, 32-20 or maybe 38 S&W or 38 Special Assuming that 32 rimfire ammo, what would you suggest to get them shooting? Rechamber to centerfire, and/or rebore and reline to other calibers come to mind. Suggestions?

I think I would try to rebore to 38 special, and convert to a centerfire breech block. I think 38 special 148 wadcutter target loads would be a lot of fun, and readily available.

If the Hopkins & Allen is a Model 932,

some in .32cal had 2 positions on the link betw the lever and the breech block.
Changing the position by moving the exposed pin when the lever is open/breech block is dropped,,moves the closed and locked position of the breech block up or down a bit.
That positions the firing pin in either the 32RF position,,or the 32CF position.

The 32CF cartridge that those rifles was chambered for was the 32COLT cf.
Kind of hard to find now.
But an easy chamber clean-up with a S&W 32 Long reamer will make the rifle into a usable caliber.

This eliminates changing the FP over from RF to CF in a conversion,,but not all of the Mod 922 H&A 32cal rifles were fitted with this feature.

Having a nice bore to start with is a good thing too.!

The Model 938 was the same rifle but in 38 cal.
The 2 cart were the 38RF and the 38S&W cart (not the 38 Special).

The action is strong but still a cast mallable iron one. IF I were to go to 38Special, the loads would be very low pressure ones for sure.

I would stick to .22rf, 32S&WL Reasonable loads.
They did use the action to build a Model Jr Schuetzen rifle and chambered it in 25-20Single Shot round, (Model 3925) or at least it was cataloged. At BP loadings,,maybe. Not smokeless, not for me anyway.

Which Remington Rolling Block action ?

The # 2 action is a solid frame and large enough to rebuild into a 38 Long Colt/38 Spl

A # 4 action was made in 2 types of take down, and neither of those should be converted into a centerfire
The # 4 action was also made in a solid frame, and yes converting the breech block, and reaming the chamber and you have a really nice 32 Smith & Wesson caliber

J Wisner

Here are photos. The H&R is marked 32 R so I don't believe it's a convertible. The Remington isn't a takedown.

https://postimg.cc/gallery/R3zjvmn