The world around us revolves around the system of rewards and punishments. Right from the religion to ordinary dealings in one's life, the foremost motivational factor either remains the fear of punishment or greed for some reward. Why would our children be any different? Nevertheless, the choice of words like bribe and fear may take some minds to defensive mode without realizing the fact that no matter what title you chose, a reward remains a reward. This reward may even be as simple as his / her favourite candy or as taxing as an extra visit to the zoo.
Those who object to motivate their children by offering them with some reward, tend to challenge the wisdom of the Almighty Creator (God). The one, who wrote the user's manual of the complex minds he created, chose to bribe the mankind, with news of pleasant life after death, if we obey his commands during our earthly life. Why shouldn't we follow the same scheme to keep the young souls on track? In fact that is what works best. I have yet to meet some parents who would not use this methodology intentionally of unintentionally. It comes natural to parenthood.
I believe that parents are responsible for preparation of their children for the challenges of practical life. One thing that they must learn is to value hard earned money in their life. From that perspective, there is no harm in rewarding (bribing) your children with some petty cash, for their hard work. This will also teach them the basics of usual relationships of employee and employer in their lives to come. It is most certain that if your child is offered a reward, he would usually negotiate its terms. He would also utilize his previous experiences and try to score better terms next time. He also learns to take responsibility for the things he was paid to do. In short - rewarding him with money for his hard work would always be a lesson for his practical life, that is not going to be very different.
I would summarize my argument with the note that bribing your children is synonymous to rewarding your children for all practical purposes. It would be very natural to reward your child for his good deeds and hard work as we expect the same for our selves from the heavenly God (the Almighty) as well as the worldly gods (mostly our employers). Most importantly, bribing your child would be rewarding for him in his life to come, in many ways.