Tether costs around $1 most of the time, but not always so. If I’m not mistaken, its price is near $1 because its issuer is prepared to buy it at $1, or sell it for $1 in large quantities. Anyone who attempts to sell it for less or buy it for more, will not be competitive in the market.
To achieve the same, you could enter very large orders of your coin in your market around the price you want to set. Of course you would first have to own these coins, but since you are issuing the coin, you should be able to do this easily.