You might consider price promotions which would include activities such as games, draws and competitions. One benefit is that costs can be calculated fairly precisely before this type of sales promotion.
Games are one of those activities which has become far more elaborate since marketing has become digital; so traditionally a game might be a bingo card or a crossword puzzle, but today the game can be a digital activity undertaken online. Obviously, there are cost implications, since we know that simple paper-based competitions are far cheaper than their digital counterparts.
Draws would be simply a lottery style activity where customers are given a ticket with a number, and when the draw happens some lucky customer will win prizes!
Competitions, unlike draws, will need a level of skill in order to win. A competition might be a quiz on a specific subject. Whichever giveaway you decide to go for, try to keep it as focused on your target customer, and your products and services, as possible. For example, if you have a cosmetics-based business, ask questions or set tasks in relation to hair and beauty.