What is the most efficient methods I can depend on to persuade a supplier about my point of view in a negotiation?

Supplier history with your company.
Facts about Supplier - Company Size, Strengths, Weaknesses, Focus Areas.
Supplier should know that you are the decision maker

In consultant procurement  QCBS  and CQS methods gives you the right to negotiate with the consultant after the evaluation of the technical proposal

In direct contracting due to genuine exigency or only this good lies on specific hand in the third world  this give you the right to negotiate with the supplier  

The world esp business world is always driven by the notion "what is in there for me?".
So while arguing and asking the other party to agree to your point of view, do let them know about the positive side for them.
There are a very few situations where it is advisable to use commercial muscles but if it is inevitable, then go for it but very very carefully.

Gather as much information as possible about the supplier.
When negotiating with supplier or anyone for that matter, "Information" plays a key part.
If you have important information about the supplier and the supplier do not have key informations about your firm, then you can use it as a leverage in your negotiation.
But make it look like it is a Win - Win situation for both the supplier and your firm. 

Different situations will require different methods depending on various factors.
Following answer is for one of the situations :  The most efficient method in this situation would be the concentration on weakness points of the suppliers proposal and ignoring any points of strengths in the proposal.
Stressing importance of compliance to the terms and conditions and could it affect the decision making in terms of selecting the appropriate proposals, In other words, you should make the supplier feel that if he doesn't show enough flexibility you might move to the next proposal.
 

Supplier should know that different situations will require different methods depending on various factors; supplier performance with our company, supplier prequalification; emphasizing importance of compliance to the terms and conditions, and could it affect the decision making in terms of selecting the appropriate proposals, In other words, you should make the supplier feel that if he doesn't show enough flexibility you might move to the next proposal; finally the more the knowledge about the product and producer the more you gain.
 

should have an idea about the product which you are going to negotiate with; the more the knowledge about the product, the more you gain.

money is the key of everything, supplier must know that you had alternative offers  better than him 

i think if you offer good payment terms, you can get good offer in the term of price 

Following points need to consider while negotiation -

 

01) Need to have the deep knowledge about item 

02) While negotiating the price - check the current market price and negotiating currency fluctuation which will give the advantageous on negotiation

03) Need to refer the final cost breakup which is helping you decide while negotiation

04) Should have alternate source to compare the price 

05) Quantity to be consider while negotiation 

05) Vendor rating - Performance of supplier in negative side or positive side 

 

06) Need to know the weakness of supplier on which we can insist more