The key thing is not to exert too much pressure. Of course, competition is inevitable, but if a price war breaks out among suppliers or your quality specifications are undermined, the lowest price is not necessarily the best. It leaves a feeling that one party has been cheated, or even a hint of distrust. This can damage your actual working relationship because there will be no room for manoeuvre, or virtually none, if discrepancies arise in the short term. This is not ideal, it is not a win-win partnership.
Negotiating is a skill that has to be learned, and serious procurement processes have nothing in common with haggling in an oriental bazaar. The ground rules are: Keep the details of the offer in mind and prepare well for meetings/site visits (e.g. Are there alternative booking methods that are cheaper?). Put your cards on the table and say that you are the actual organiser rather than an agent. Then commission (a potential cost factor) will no longer apply.
Always remember that the written word is final. Agreements are only 'watertight' when they are enshrined in a contract – particularly if the conference/convention is not to take place for another one, two or three years. Two heads are always better than one, so get legal advice if necessary, particularly when negotiating extras such as currency hedging and tricky cancellation terms which could otherwise break the budget.