I'm throwing a birthday party for a friend tomorrow.

Literal

Tomorrow, friend [possessive-の] birthday-party [object-を] open.

Standard 会を開く pattern for hosting an event. 誕生会 ('birthday gathering') is slightly older or more childlike vocabulary than the current 誕生日パーティー. Note how the possessive 友達の attaches to 誕生会 — 'a friend's birthday party.'