The Romanians used a single-shot, bolt action Model 1956 training rifle and the more often seen Model 1969 bolt-action 5-shot repeater.

There are unconfirmed reports that a version of the AK-74 in .22 Long Rifle (sold in a commercial variant in the states as the AKT-98 imported by Armamentos in Florida and the WASR-22 by Century International Arms) is currently in use as a training rifle.

These were manufactured at Cugir.

Poland used the single-shot, bolt-action Mosin-Nagant Model 1944, rechambered in rimfire and given the Model 1948 nomenclature. The Poles also built some Type III milled receiver AK-47's up in .22 LR for use as trainers.

Bulgaria built the RKKS .22 LR version of the Type III AK-47.

The East Germans built a select-fire AKM/AK-74 variant trainer in .22 LR, the KK-MPi Model 1969 . The sub-caliber magazines were sold here a few years ago and several parts sets were imported by Interordnance. At least one set was built up as a PMDS and was offered for sale maybe three years ago.

The russians use a suppressed, crank-bolt action, folding stock version of the Ihzmash Biathlon rifle as a short range sniping rifle. The designation is SV-99.

Modern Firearms - SV-99 sniper rifle

I own a TULA TOZ-78 (also sold as the Winchester "Wildcat" model here). As far as I know, these are only commercial sale rifles. They seem to be very good shooters, but I don't know that were actually used as military training rifles.

TULA, Ihzmash and Baikal all built various target/match type rifles that may or may not have been used by military rifle teams. While many of these are advertised as 'trainers', the claim is often hard to verify.