A large rifle primer is too large for a 30 carbine case, so it won't fit.
I've read many accounts of folks using small pistol and small pistol magnum primers in small rifles, but I've never tried it myself, so I can't comment from personal experience. From what I've read, the cup is not as thick in a small pistol primer than in a small rifle primer. Therefore, using a small pistol primer in a high pressure small rifle case could result in a pierced primer cup.
The one exception that I know of is Rem small rifle 6 1/2 primers (as opposed to Rem 7 1/2 primers). These Rem 6 1/2 small rifle primers are not indicated for use in high pressure small rifles such as 223 and others. It says so on the box. Primer cup piercing is the risk since they have thinner cups. These particular small rifle primers are, from what I've read, interchangeable with with small pistol magnum as the thinner cup allows for reliable ignition in revolvers. On this point, I do have personal experience: I regularly use Rem 6 1/2 primers in my small pistol magnum loads. I can't feel/tell the difference but I've never chronied them for comparison. No issues whatsoever.
I also load my 30 carbine with Rem 6 1/2 small rifle primers. I've never had an issue doing that.
Bayou