This is going to be an arduous endeavor and one that may require you to have a breeder's license. Many states, New Hampshire included are falsely labeling Mute Swans as an invasive species and are trying to kill them or prevent them from producing any offspring. Therefore, if the wildlife officials do not kill or remove the remaining swan, it is highly unlikely that they will want any cygnets produced.

But, let's say that you do get a breeder's license, then you will need to do the following:

Capture the swan and ensure that it is indeed a male so that you will know for sure before introducing a new swan into the habitat. If you introduce a same gendered swan, this may result in serious injury to one or both birds from fighting. Your swan is not going to accept another male. It is also questionable if the swan will accept another mate (female) as most male swans will not re-pair with another swan and choose to live their life alone after losing their mate.

Then, you must build a pen (1/2 on land with a zero entrance and 1/2 in water) completely enclosed top to bottom to prevent any predator from digging under or climbing over into the pen and attacking the swans. You also need a zero entrance from the land to the water so that the swans' legs/feet do not get injured.

You will need to place a feeder inside the pen so that the new bird can get used to you (the caretaker) and the feeding system. The pen allows the swan to familiarize itself to the new habitat and allows both swans to familiarize themselves with each other. The new swan must be kept in the pen for approximately 1-2 weeks so that you can monitor for any defensive behavior. If such behavior is present, then the two swans are not going to get along and to still introduce them may result in serious injury to one or both of the birds.

Prior to introducing any swan, ensure that you are receiving a swan from a reputable breeder who can provide you with licensed veterinary documentation showing that the swan is in fact the gender that you are purchasing, it is pinioned (rendered unable to fly), and has all veterinary care/vaccinations etc., as mandated.

Even after going through all of this, there are no guarantees that your swan will ever accept another mate. We would strongly suggest leaving the stable situation stable and not trying to introduce another swan which may actually create more problems. The Regal Swan