Photo would be useful here - red and green berries all year? Weird... many berrying shrubs have white flowers in Spring, not many have berries all year, whatever colour they are.

Wild guess without a pic, but could it be a Skimmia? The unripe berries are green and visible for quite a bit of the year.

Difficult without a picture, and specific times (all year?), but what about buckthorn, the fruit of which is quickly formed, and takes a while to ripen, ofen with berries at various stages. Flowers are small and greenish, though.
Phil J

Ah, had a thought - nandina domestica, that might fit with the berry thing. Try looking that up.
Phil J

Nandina doesn't work too well with the "lemon-shaped" leaves. though. Maybe one of the smooth-leaved holly hybrids?

Could be one of the Cotoneasters even....