What can be done when a ritual asks you to bury remains and such in your backyard but you don’t have a back yard? Is there something that can be done alternatively? Or what would y’all recommend 
Almost without exception, ritual burial only need entail that you are returning things, symbolically, to the earth and the powers therein. It doesn’t really matter that you “own” the imaginary line around that particular patch of earth- you’re making a clear gesture that you appreciate the role of the parts you’ve used for your magick, and are giving back what’s left over.
It sounds like you’re talking about the remnants of spent spell materials, which you want to dispose of in a non-dismissive manner. You can go to any local park or natural area, roadside, or whatever. What matters is that your leftover spell bits are still being treated as special, rather than going in a bin with the normal trash. If you never plan to dig it up, you can bury them anywhere to decompose.
This goes double for any sort of ritual which involves a burial as part of the rite itself, such as a consecration of a spirit-vessel in which your tool is going into the ground and coming back out later in symbolic rebirth. You can use any earth, even if you have to go so far as to use a houseplant, just to keep track of exactly where you buried it.
Hope this helps. 
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