Remove poultry necks and giblets and reserve for other uses, if desired.
With poultry shears or a knife, split each bird lengthwise along one side of backbone.
Place birds, skin side up, on a flat surface and press firmly, cracking bones slightly, until birds lie reasonably flat.
Rinse birds, pat dry, and place in a large heavy-duty plastic bag.
In a small bowl, combine apple juice, lemon juice, oil, and fennel seeds.
Pour into bag over birds.
Seal bag securely, rotate to distribute marinade, and place in a shallow baking pan.
Refrigerate for at least 4 hours or until next day, turning bag over several times.
Lift birds from marinade and drain briefly (reserve marinade).
Arrange birds, skin side up, on a lightly greased grill 4 to 6 inches above a solid bed of medium coals (for game hens) or hot coals (for squab).
Cook game hens until meat near thighbone is no longer pink; cut to test (30 to 40 minutes).
Cook squab until skin is browned and breast meat is cooked through, but still pink near bone; cut to test (15 to 20 minutes).
During cooking, baste birds with marinade and turn often.