If it is actively dangerous for them to be around me then I wouldn't worry about cheering them up, assuming that they are staying to help you regardless doing anything positive would only reinforce the fact that you are worth helping in the first place, which is counterproductive to driving them away.
Unless your game has a main hub world where the characters gravitate for story reasons the easiest way I can think for the character in danger to accomplish his or her goal would be to wait for the character they don't want to endanger to fall asleep one night and then just leave them, or take it a step further and have them spike that character's food so that they won't be able to wake up and pursue them in time to catch up. Either way this establishes distance as well as evoking feelings of betrayal that would be at the forefront of this person's mind when considering whether to pursue their friend further and make the idea of "forgetting them and leaving them to their fate" feel like less of a betrayal for all but the closest of relationships.
If they are bound to a hub or the friend is an expert hunter/tracker or something then
@RetroBoy has the right idea I think. Answer any question that can be answered with a yes or a no as such, and simply keep silent when confronted with any question or statement that requires more than a one word response. The vast majority of people in this world cannot stand extended periods of silence, and this revulsion is doubly felt when they are speaking seriously with someone. It'll drive most people away faster than verbally assaulting them (where they can compartmentalize the abuse and get over it for their friend's sake) would.