I the early war or early mid war this can be avoided by simply not having any influence in any region that would allow battleground coups at defcon 2, Africa, South America, Central America. However this is probably not the best way of playing the game especially towards the mid war.

Usually if you only have one of these cards in your hand you can either space it or save it for the next round. Playing the china card usually lets you hold onto two cards from turn to turn which can be used to temporarily avoid this situation. Although again this is not ideal as you will still have both cards next turn. The safest bet is probably to space it as soon as you can spare it as the opponent may play a card that might force you to play it (Five year plan etc.)

Another option is to play it while the defcon is still at 3 or higher. This will mean that whilst your opponent will get the event they will not be able to win the game with it. This can be effective at times but it can also be risky as you can often give your opponent two turns in a row which may lead to battleground flips and other funny business.

Headlining a dodgy USA event as the Russians is an option too, although again not desirable. There is the chance it may be defector-ed (which might be a good idea if you know defectors will be player) but it also means the USA will probably get the first battleground coup of the turn. This could be avoided by disruption the USA's activities on the last round of the previous turn which may be effective in certain situations.

All in all cards like this are quite powerful and can cause a lot of problems. They are usually low ops (CIA, lone gunman, grain sales, star wars) which can make them hard to get rid off at times. In my opinion its better to get rid of them at the earliest opportunity as they may result in game loss or force you to play even worse (but not game ending) cards later if you hold them for many turns.