A good tip is to go buy missing legendaries from Kharla with bloodshards. I find the ring, amulet, and second hand item to be the least common drops. You can go to her and legendaries actually pop up with some level of ease.
Just wait until you are level 70 hoarding blood shards, which you can hold up to 500 of, and just keep on purchasing the missing items until a legendary appears.
Another possibility that you can use with the expansion is getting rares and upgrading them to legendary through the cube. You get the cube at some point in Secessaron in Bastion's Keep Act III. I don't remember the exact breakdown of ingredients, but you need a level 70 rare, and then various rare ingredients that Tyrael gives you for completing an act. Especially if you complete the acts where you can get a bonus cache, you should have more than enough ingredients to upgrade the rare.
Like I said I find rings to be the rarest. Playing on both Xbox One and Ps4, with probably 200 plus hours on each, I only got about 2 or 3 ring dropped. I think if you play at the higher difficulties like torment and up the rate is probably higher, but I played at Master and occasionally Torment 1, and it was scarce.
*** One more important tip that I think is obvious but some people might not realize, you just need to have a level 70 in each slot. That means if you have a two handed weapon, it covers two slots, you don't need for example a legendary main and off hand weapon, so that saves you one slot.