I have stayed at Marriott's 2x for my birthday and was very happy! But that was at the JW Houston Galleria and NY Midtown Renaissance. Both hotels recognized my birthday.
I have not stayed at CY for my birthday, but they might do something if you let them know you are celebrating!
Be sure you have your b-day listed on your Marriott Rewards acct.
We've had various offerings when the hotel knew we were celebrating either a birthday or an anniversary. Cakes, dessert trays, champagne, wine, cheese trays. Have only had these types of things at a full service Marriott(JW, Autograph, Delta, Marriott etc) so don't know about Courtyard, Residence Inn, Springhill or Fairfield. Let them know when you are making your reservation and let us know if anything suprising happens.
We haven't stayed at any Courtyards on birthdays but I have had special treats at two Autograph Collection hotels, a Renaissance and a Marriott. We were doubly impressed by the Renaissance that noticed that our youngest was wearing an "it's my birthday" button and they sent balloons and a slice of cake to our room for her.
IMO, a birthday is a great day to spend at a Marriott as long as you are not working and not alone...But then again I don't actually need a lot of encouragement to find an excuse to stay in a Marriott
Just to avoid any disappointments: hotels don't have any obligation of any kind to do something for your special day.
That being said: I'm sure that hotels (even CYs) will do an effort to offer something to underline your celebration. It's an important part of the client experience and will be paid back through the word-of-mouth marketing and potential on-line reviews.