Like it says on the tin:
What's going on with the stone and Japanese text here in Sandman No. 36?
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Greg Morrow's very early Annotated Sandman for Issue 36 (v2, 14 February 1992) includes the information:
Page 19 panel 1: The Hierogram (Holy-Writing) is marked with Japanese katakana (one of the Japanese alphabets). The characters spell out "do-rii-mi-n-gu", or "Dreaming". The leftmost side of the first character should have a vertical stroke, not slanted, and the last character should have only two tickmarks on the side, not three.
There is a Cuckoo Stone in England, which may have influenced this denouement. There is a legend about a cuckoo landing on the Cuckoo Stone at a certain time of year.
The name of the Isle of Thorns may be a reference to the "thorn" character of Old English, a relic of runic alphabets such as Icelandic. A thorn looks like a combination of 'p' and 'b', and represents a voiceless 'th' sound. Thorns would thus be connected with the katakana letters.
Katakana's the form of Japanese used for foreign transcriptions (originally Chinese and Sanskrit works on Buddhism and now for international pop culture) and that seems to be what's going on here. The stone reads (a version of)
which transcribes Dorīmingu or Dolīmingu—English "Dreaming" or "The Dreaming", the realm of Morpheus.
The Cuckoo Stone is part of the Stonehenge Complex and doesn't seem to bear any relation to the hierogram outside of possibly having been used for sacrifice in a similar way.
Thorn (þ) doesn't seem to have anything to do with this although no actual thorns are seen on the island.