Burps, or belches, are caused by a vibration of the upper oesophagus as gas is expelled through it. This could be oxygen and nitrogen after breathing in too fast, or carbon dioxide after glugging a fizzy drink or suffering a bout of indigestion. There’s nothing about space that would cause this natural bodily reaction to stop, however there would be fewer things to trigger it.
For instance, astronaut diets are carefully formulated for easy digestion and cola would certainly not be part of it. Even if it were, carbonated drinks don’t fizz in space as there is no gravity to separate the gas from the water, leaving air bubbles simply floating in the liquid.