another ".36" rifle

Well first, if it's a .36 from EIB and a Spanish barrel, it's likely going to use a .350 ball wrapped in a cloth patch that is .015.
Your .375 ball are designed for your ".36 Revolver" because that functions by swaging the ball onto the lands of the barrel when the revolver is fired. The same principal is used with modern .358 bullets...the label ".38 special" was coined using a slightly different way of naming cartridges; the ".357 magnum" cartridge is more accurately named.... So neither the .375 ball nor the .358 bullets are going to work for you. Sorry.
As an inexpensive plinking and small game rifle, these .36 caplocks are often pretty good deals at an inexpensive price.
You should consider using 3Fg black powder, not basic Pyrodex for the main charge. Both black powder and Pryrodex P (pistol) are dirty, but 3Fg I have found for small calibers such as those under .40 tends to burn a tad cleaner.
Prior to loading, following a good cleaning, you will need to "pop" two of the percussion caps on the nipple into the empty barrel to ensure a dry, clear channel for the spark to reach the main charge.
You may also want to invest in a "nylon" or fiberglass loading rod, as the small rods on factory .36 caliber rifles are notorious for being inadequate and easily breaking.

LD

Yes, the Traditions Crockett and the older T/C Cherokee (if you can find one) use a .310 or .315 ball. The .32 is a great plinking round, and very economical. With 10 grains of 3f you get std. velocity .22 rim fire velocity, and it is usually very accurate out to 35 yards. Of course, you will have to see just what load, ball and patch combo your gun likes. Each gun is an individual when it comes to a load it likes. As a general rule, the guns with a 1:48" twist tend to shoot very well with a .310 ball, 25 grains of 3f, and a .015 patch. Your mileage may vary.

I used .311" ball from a Lee mold in my Crockett. My .36 takes a .350 ball with a .024" canvas patch. Of course the patch can be thinner if needed. It's likely a .350" ball and .015" ticking patch is a great place to start with your rifle.

There was a like new .38 caliber rifle for sale that was made in Italy.
I sent you the link to the ad in a PM.
I forgot all about it from earlier in the year, maybe it's still available.
Since it's made in Italy, it's not the same rifle and should actually be a .38 cal.
The patch box on this .38 rifle is shaped like an eagle.
I'd be very surprised if any BP rifle marked .38 or .36 wasn't the actual caliber size.

Dont overlook the popular and authentic .40caliber.
Many original rifles of our ancestors started out as .38 or .40s.
Imho the .36 and .40 shoot cleaner than the .32s....but that's me. I've not had anyone agree with my theory, lol

Here is an original. 40 that began as a .38.

The .40 is a popular caliber among benchrest bp shooters too.

The 'old guys' at my club swear by their .32s and .36s.

I have owned a couple of 36 caliber rifles and shot them with .350 round balls and also 38 wad cutter hollow base bullets. The same bullets used in 38 Special target loads and the bullets slip right down the bores and then act just like flat nosed Minnie' balls. They shot very, very well for me. So don't give up on a 36 caliber gun. At most you might have to buy a couple of boxes of .350 balls. Of a mold. No big deal.

I have shot 32s and much prefer the 36. The 40 might be even better. A while back Dixie had a Pedersolt .40 for sale cheap. And I already cast .390 RB for making 3 ball loads in my .410 shotguns.