If you are a colonial Loyalist as the conflicts that eventually lead to the Revolution are beginning to build, how would you persuade those pushing for independence and war that it would be best to remain a British subject? (Be sure to address specific complaints that rebel colonists had against British rule.)

One argument the colonists who wanted to break away from England made was that they were subject to "taxation without representation" because the colonies were not represented directly in the British Parliament. A Loyalist might have responded to this argument with the fact that no one in England was directly represented in Parliament; instead, the representatives in Parliament were thought to represent all the subjects of the crown.
The colonists were angered by their need to pay taxes to the British crown and by their being forced to quarter soldiers. A Loyalist might have responded that the British crown also defended the colonies and fought for colonists' protection in the French and Indian War. The British crown was a powerful military force with a first-class navy, and a Loyalist might have pointed out that the colonies needed such a force to keep themselves safe against the French.

As a colonial Loyalist in the midst of the build up to the Revolutionary War there are three important factors to take into consideration in attempting to persuade those pushing for independence to remain British subjects. First, it’s important to understand the specific grievances of the would-be revolutionaries. Luckily for us these grievances are pretty well enumerated in the Declaration of Independence. There’s no need to discuss each specific grievance, suffice it to say that the central theme of the complaints center around the policy decisions of King George III regarding the American colonies. Secondly, it is important to understand that in the mid-18th century nearly all governments of the world were monarchies and England the premier among them. The idea of representative democracy as we know it today was as abstract a concept as there was. And thirdly, thanks to the Magna Carta, even in the mid-18th century the British Parliament held considerable power in the British government, and even well before the fateful publication of the Declaration of Independence members of parliament such as Edmund Burke were openly criticizing King George’s policies regarding the American colonies (specifically tax policies)—policies that the revolutionaries themselves cited as grievances against the King.
With these factors taken into account, arguing the pragmatic approach that remaining subjects of the foremost economic and military power of the world and advocating for change to members of parliament through activism would be much more likely to result in positive change and address the grievances of the Patriots than embarking on a path of complete uncertainty would. As a matter of fact, this was the line of argument that was indeed advocated by many British Loyalists such as Thomas Hutchinson who agreed with many of the Patriots complaints regarding tax policies but disagreed with Independence being the best way to address these concerns.

One of the main grievances of the colonists was the stationing of British troops on American soil, by which they felt intimidated and which they believed would be used to suppress liberty. If I were a Loyalist, I'd argue that a push for independence would not solve this problem, but only exacerbate it. It would give the British an excuse to send even more troops across the Atlantic, and what would become of American liberty then?
The colonists were also angered by Great Britain's imposition of various taxes, such as those introduced under the notorious Tea Act, which led directly to the Boston Tea Party. As a Loyalist, I would argue that, although it's understandable that colonists should be upset at such impositions, trade with the mother country is generally very beneficial to the colony. America is only prosperous due to its trade with Great Britain; but if it decides to proclaim its independence and go it alone, that prosperity will be under serious threat. In the event of independence, the British will use its vast navy to blockade America, making trade with the rest of the world almost impossible. The economic consequences for the country would be dire indeed, certainly far worse than anything that could come about due to excessive taxation.

I would first appeal to their sense of nationality. Technically, the rebels are British citizens, and by going to war against Britain and the crown, they are committing treason. From this point of view, they are the "bad guys." One of the specific complaints of the colonists was about taxes and representation (or lack thereof). Going to war and making a break with Britain isn't going to get them any kind of representation. There is no guarantee that a colonial government would be any better or different. I would continue to stress the importance of finding non-violent solutions to their complaints. I would also remind the Patriots of the strength that is the British army and navy. While the colonists might want independence and are willing to fight for it, they are in all likelihood going to lose that fight. The colonists might respond by talking about their strength in numbers based on the number of colonies, but the colonies and the British crown are stronger together than separate.