According to Marx in The Communist Manifesto, what is the relationship between revolution and violence?

For Marx, the relationship between violence and revolution is one of necessity. Quite simply, he believed that if the bourgeoisie would not voluntarily hand over the means of production, then the proletariat would have to take it from them violently. This is shown clearly in the closing paragraph of chapter 2 when Marx talks about taking "by force" the bourgeoisie's power:

If the proletariat during its contest with the bourgeoisie is compelled, by the force of circumstances, to organize itself as a class, if, by means of a revolution, it makes itself the ruling class.

In addition, in the final paragraph of chapter 4, Marx makes another allusion to violent revolution, as part of a call to action to those who are reading this pamphlet:

They openly declare that their ends can be attained only by the forcible overthrow of all existing social conditions.

What we find, then, is that Marx advocates violent revolution. For him, violence is an acceptable means of revolution if it guarantees his desired outcome. That desired outcome is the abolition of private property and all class distinctions across the world.
In other words, if the proletariat wants to take power, they must be prepared to use violence in order to make this possible.