If the "Adopt" option is missing from the Services menu in The Sims 2 (PS2), here's the likely cause and fixes:
Adoption requires The Sims 2: University expansion data on the disc. The base PS2 game does not include adoption. Only the "The Sims 2: University" standalone PS2 release (or the "Double Deluxe" PC bundle) has it. The standard PS2 The Sims 2 disc lacks this feature entirely.
If it's still missing with University disc, the disc may be mislabeled or damaged. Compare disc ID: SLUS-21166 (Base) vs SLUS-21612 (University) for NTSC-U.
Bottom line: Standard PS2 Sims 2 = no adoption. You need the University edition.