"overly eager" is correct and can be used in written English.
You use it when someone is excessively or overly enthusiastic about something. Example: John was overly eager to start his first day of work.
Years of social rejection had made her, in his view, overly eager to please.
Maybe you think others will see you as overly eager, an aggressive and ambitious attention hound.
There are signs the US is not overly eager to strengthen the opposition, however.
Mr. Mooney worries that the center is overly eager to work with big biotechnology companies like Monsanto and Novartis.
Frankly, we are concerned about President Karzai's overly eager determination to hold a tribal council on reintegrating Taliban leaders, including the chief, Mullah Muhammad Omar.
From a more technical standpoint, my research suggests that one should not be overly eager to chase down the latest trend at this stage of the campaign.
This is good, except that a host may be overly eager to impute abstemiousness to his female companions, perhaps to his own advantage.
Mr. Phillips confirmed that Ms. Rice had been interviewed, but disputed any notion that she had been overly eager in seeking attention for her work.
This will hopefully drum up some additional investment from the more gullible sections of an overly eager West while they wait for a resurgence in commodity prices.
If Lizzie Bennet were alive today, her greatest fear would not be an accidental pregnancy but an overly eager suitor who might distract her from writing her novel.
These plush centres were built on the wrong side of the property boom by overly eager developers looking to create retail meccas.
