My mom taught me this one and I have had many a parent thank me for the thoughtfulness. First off, make sure the sibling is old enough to even care that it is not his/her birthday, otherwise hold off until they are older.
Small, wrapped gifts that you can hide in a purse, pocket or bag work the best. Always make sure the gift is age appropriate. It is also nice if it will keep the sibling occupied. I have had good luck with individually boxed toys from Playmobil and the Nerf Pocket Vortex Football