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Any black powder ammo is quite rare. Even famous black powder cartridges like 45-70 are hard to find factory loaded with black powder. Having someone load them has it's liability issues attached to it and most people I know who reload wont reload for others.
Any specific reason why you are looking for black powder 7.62x54R? As far as I know it was never a black powder round; it's been smokeless since it's introduction in 1891. I know the 303 British was originally black powder for a very short period of time but I've never read the same about the 7.62x54R.
I looked up "3-line" and what I found implies they where precursor or prototype cartridges and rifles before the development of the Mosin Nagant. I can't find too much info on them.
Regardless I know of the appeal of black powder in things that aren't commonly black powder or where black powder gives no benefit other than an emotional one. I load paper patched cast bullets over black powder for a 45-70 and have done some 303 British black powder as well just for fun. I also love Hickok45's video about black powder 45ACP in a Glock on YouTube.
I don't load ammo for others as I don't want to get involved in any sort of liability.
I know in many states black powder falls under explosives classifications instead of the propellant classifications that smokeless does so it can be very difficult to get black powder or black powder cartridges some places. Since most of our ammo comes out of the US that could effect our supply as well. I would say that since most BPCR shooters handload so they can tailor components to their rifle and preferences there is very little demand for black powder ammo in Canada. Add to that different storage and transportation requirements compared to smokeless ammo and it just isn't worth the trouble to bring it in. Most stores wont even carry black powder because of the extra storage requirements. I get mine from the range I shoot at and they have to store it in a shed on the edge of the property while smokeless powder is on shelves in the back room.
Thanks for the very informative (however dream shattering) responses. I was curious about black powder in the 7.62x54r cartridge after seeing a few videos online of people using black powder loads in Mosins and thought it would be a lot of fun to try out. I guess I'll just have to get into reloading eventually.
I've seen a Mosin torture test by iraqveteran8888 on YouTube where they used black powder in a cartridge and it worked. Don't think I would try it myself, though.
*EDIT* - I should note they mentioned not to "try this at home."
Highly unlikely you'll find BP ammo for a cartridge that never used BP.
3line cartridges were just Imperial Russian designations that meant .30.
Reloading commercially without a Federal licence is illegal. There will be no BP load data for a 7.62 x 54 anyway.
Do not copy what you see on places like Youtube. Bubba lives there.