For an expansion joint that is 7/8" to 15/16" wide, you should use a backer rod that is slightly larger than the joint width to ensure a snug fit. The general guideline is to choose a backer rod that is about 25% larger than the joint width. Given your joint width: 7/8" (0.875"): A backer rod around 1-1/8" (1.125") in diameter would be suitable. 15/16" (0.9375"): A backer rod around 1-1/4" (1.25") in diameter would be appropriate. Therefore, a backer rod with a diameter of 1-1/8" to 1-1/4" should work well for your expansion joint