Short answer. Yes, for an adoption entry specifically. Rule 108, Section 2 lists adoptions among the entries in the civil register that may be corrected by court petition for good and valid grounds. Republic Act No. 9048 and Republic Act No. 10172 moved only clerical corrections to an administrative route; substantive entries like adoption still require this judicial proceeding.
What the law says
Upon good and valid grounds, the following entries in the civil register may be cancelled or corrected
Rule 108, Section 2 — Entries subject to cancellation or correction. Read the full provision →
What the law says
(g) legitimations; (h) adoptions; (i) acknowledgments of natural children
Rule 108, Section 2 — Entries subject to cancellation or correction. Read the full provision →
Adoption is named directly among the covered entries
Section 2 lists the entries this proceeding reaches: upon good and valid grounds, the following entries in the civil register may be cancelled or corrected. Among the items in that list are (g) legitimations; (h) adoptions; (i) acknowledgments of natural children. Adoptions are named specifically, so your adoption decree falls within the entries this rule was written to address, not left to guesswork about whether it qualifies.
Why this still requires the judicial route, not the administrative one
Republic Act No. 9048 and Republic Act No. 10172 later opened an administrative path through the local civil registrar, but only for clerical or typographical errors, a change of first name, and the day, month, or sex entry where the error is clerical. Annotating an adoption decree is a substantive entry, not a clerical correction, so it remains within the judicial proceeding this rule describes rather than the administrative shortcut those later laws created.
This still requires 'good and valid grounds'
Being listed among the covered entries does not make the annotation automatic. Section 2 conditions the correction on good and valid grounds existing in the first place. So the question is not only whether adoption is the right kind of entry, which it is, but whether the underlying grounds for the annotation you are seeking are actually good and valid ones. Nor does the rule rank or enumerate what those grounds are; whether the decree, the entry it affects, and your supporting papers add up to a sufficient ground is decided in the proceeding itself, on the strength of what you present.
What this means for your adoption decree
Because adoption is named as one of the entries Rule 108, Section 2 covers, and because that entry does not fall within the narrower clerical-error route RA 9048 and RA 10172 created, this kind of court petition remains the applicable proceeding for annotating your adoption decree in the civil registry, provided good and valid grounds exist. Note the limit as well: the petition operates on the registry entry itself; it is a means of making the record reflect the decree, not a vehicle for attacking or re-litigating the adoption.