The topic line suggests that you are writing about "The Yellow Wallpaper," but the prompt you include refers to "The Tell-Tale Heart," so I'm not sure which story you want help with. Whichever story you address, the goal of an alternate ending is to find a different resolution to the conflict that the story has set up.
"The Yellow Wallpaper" ends with the narrator descending into madness because that is the only way that she can take control over her own life. One way to change the ending is to figure out another way that she can escape her husband's control, such as having her flee the house and set out on her own. Another way would be to have John enter her delusional state, to have him "see" the woman in the wallpaper too, so that the tables are turned as the narrator gains power over the husband.
For "The Tell-Tale Heart," one obvious alternate ending would be for the narrator to keep his cool when the police are in the house and for the police to leave, satisfied that there has been no foul play. You could either end the story by describing the narrator's sense of triumph over his deception or bring about his undoing by other means, such as having him so tormented by the "beating of the hideous heart" that he kills himself to escape it.