What To Say
Anyway here are my personal observations of good and bad things to say to singles.
A rule of thumb is that anything you would not say to a childless couple about being childless you should try not say to a single person about being single. Thus saying at a wedding “you are next” or “soon by you” has lost much of its appeal. Personally I think it is fine just to say “It was very nice to see you. All the best to you” just like you would say to any other adult. If you feel an irresistable desire to give them a bracha may I suggest “May Hashem grant you all that you desire” or “May Hashem bless you with success in all your endeavors.” If you say something specific about getting married then the single person may indeed interpret it to mean that you do not value all the other good things in their life such as their job, friends, hobbies, service to the community, etc. as has been mentioned in the comments.
If you want to set up a single person may I suggest that you first make sure you know something about them and what they are looking for? It is fine to call and ask them! This will show that you are making a thoughtful match and not just putting two people together because they are both frum and near each other in age.
If the single person has been complaining to you about being single then it would appear this is a single you know well and who trusts you so you do not have to be as worried about saying the wrong thing since it appears you are already friends and you tend to say the right thing to them! But here is a suggestion. You could say “You deserve to be happy and since you want to get married so badly I hope you get married soon. Meanwhile I am happy that you are my friend because you are a great person and the world is a nicer place because you are in it.” In other words to say that you hope for them the same things they hope for themselves but also to remind them that their existence has value even if they are single. Personally I like it when a friend (or commenter) tells me they are davening for me but that is because we are friends (or because I have opened myself up on the blog). I do not think I would like it if a person who hardly knows me told me in shule that they are davening for me. I would rather they daven for me and not tell me!
I agree with the commenters that setting a person up is much more helpful than just giving them a bracha but may I add another suggestion. Inviting a single person for Shabbos meals is also very nice and helpful to their lives even if it does not directly help them get married. You are still doing a chessed for them. Even if it seems like they always go away for Shabbos or have plans and you say “the next time you need a meal just call me” then still keep inviting them anyway. If you rely on them to call you they may be too shy or embarrassed to “invite themselves.” If you keep calling them then they will feel more welcome as opposed to one time being told “call me if you need a meal” and then never hearing from you again.
(By the way I think singles who have space should invite back families who hosted them. It is hard to cook for so many more people and childproof the house but if a family has had you over many times then it is time to invite them back! Even if they say no at least you tried. I am saying for Shabbos meals not to sleep over for all of Shabbos.)
People do not like to think that they have disappointed their parents by not getting married. If you have a child who is single then a nice thing to do is tell them “I am proud of you.”