Might be worth having a look at flying into Vilnius and either train/bus from Vilnius to Minsk. You might even get a decent deal with a taxi as it's 2.5 hours drive.
i remmbered rometorio.com and damn, i think its actually improved.that gave me a bunch of options for going to minsk2 years ago when i used it, it often pushed car sharing as an option maybe? but was pulling wrong dates n stuff so you would be waiting weeks for that car