The answer is yes. However, the large commercial ammunition makers usually make the majority of theirs for military training, with the rest usually absorbed by law enforcement and theatrical use. You'd have to check with the current listings of Winchester or Remington to see what's in current production.
Military surplus blanks are available from various dealers, but they're usually in calibers such as 9mm or 5,56mm or 7,62x51mm or 7,62x39mm or .30-06.
Then there are the small outfits that load blanks in just about every caliber for training or scaring off pests. Other outfits load them for the entertainment folks -- Hollywood and TV production. Or, with a little ingenuity and an inexpensive loading press, you could load your own. RCBS makes blank reloading dies.
Some things you need to know about blanks.
1. They're DANGEROUS! In 1984, TV actor Jon-Erik Hexum accidentally shot himself in the head with a .44 Magnum prop gun on the set of the CBS series Cover Up. The wad from the blank drove bone shards into his brain. In another instance, a WW2 reenactor shot an 8mm wooden tipped blank (designed for machine guns equipped with a special kind of blank addapter equipped with a shredder) in a standard Mauser rifle. The wood bullet had hardened with age and performed exactly like a ball round. Fortunately, the reenactor who was shot did not get seriously injured.
2. When it comes to military rifle blanks (some pistol loadings, too), you can find them with paper wads to hold in the powder, or wooden bullets (for submachine guns and machine guns) or a crimped nose or plastic cases. The most dangerous are the wooden blanks that harden with age and are designed for specialized BFA (blank firing adapters). Plastic blanks are designed for cheap manufacture and one time use. Most U.S. blanks have a cardboard wad in the end and the wadding itself is dangerous at close range. Some blanks have tapered and crimped noses to aid feeding in firearms, such as the M200 5,56x45mm NATO blank.
3. Do not confuse blanks used for training with grenade blanks for launching rifle grenades. The grenade blank is a VERY powerful blank that's designed to project a rifle grenade out to about 400 yards. They are usually identified (at least the U.S. ones are) by a 5-petal rose crimp on the case. The grenade blank will not harm a firearm unless it has been fitted with a BFA. Then the blank may blow-off the BFA or damage the firearm from the extra pressure generated.
4. Military blanks vs. "Hollywood" blanks. Military blanks are primarily used for training. The main concern is to cycle the weapon in which they're used and to simulate the actual noise of firing. The .30 and 7,62 NATO caliber blanks are very loud in comparison to the smaller 5,56mm NATO blanks. "Hollywood" blanks are enhanced with compounds designed to produce large muzzle flashes for the camera. These blanks are specially loaded by prop houses to be loud and produce large flashes -- especially those shot through fully automatic weapons. On some prop guns, the flash is so bright you could read a newspaper at night.
5. All of this is the long way around in saying -- yes, you can buy blanks for your particular firearm. Someone loads blanks for your firearm somewhere. Someone has loaded blanks they'll sell to you. The usual question is how much? The cost of theatrical blanks will astonish you. They may be even more than live ammunition! Military surplus is available, but the caliber selection is limited to those used by the military and there are some safety issues to be observed.
If you have a self-loading firearm, to make it work as it was designed, you will have to use a BFA. Some firearms, like the .45 Auto don't like to feed blanks reliably without specialized work that prevents the firing of live ammunition. Most of the time, Hollywood uses .45 Auto look-alike prop guns in 9mm that work better (and usually go unnoticed by viewers). Revolvers and other manually operated firearms don't have to worry about this, because the shooter provides the muscle to make them function.
If you're having problems finding blanks in your particular caliber, you can always load your own. Some WW2 reenactors do this for their arms. When I was WW2 reenacting, I made up some .45 ACP blanks with some old WW2 .45 ACP steel cases, surplus blank powder from some water-soaked .30-06 blanks, and some balsa wood as a plug to keep the powder from falling out. The rounds would not cycle my .45, but I could shoot them single shot. The balsa wood plug was disintegrated by the burning powder and I never shot them at close range or at someone.