Weird...It's working fine for me.

Can you please share the output of:

SystemInformation["Small"]
PacletInformation["ServiceConnection_GoogleCustomSearch"]

Also, when using your Google credentials, do you get that box saying GoogleCustomSearch Connected? (Like the one in my screenshot after ServiceConnect)

. The "ID" you see there is not the Custom Search ID I created through Google's Custom Search Engine page. I tried to put the ID in manually as an argument, and I get the same result (well, lack of result).

The ID you see there is not the Google ID but the internal connection ID.

I'm having trouble with this, despite getting an API browser type key from the Google Development platform, and a custom search ID. ServiceConnect["GoogleCustomSearch"] works as far as I can tell, returning a ServiceObject that is connected. But then when I do the following:

customsearch = ServiceConnect["GoogleCustomSearch"]

customsearch["Search", {"Query" -> "transactive memory", 
  "Site" -> "http://scholar.google.com", "MaxItems" -> 10}]

the second evaluation returns

ServiceObject[
 "GoogleCustomSearch", 
  "ID" -> "connection-03fd5d9f173245ebd05b0f1d96dde014"]["Search", \
{"Query" -> "transactive memory", 
  "Site" -> "http://scholar.google.com", "MaxItems" -> 10}]

No results are returned; my Mathematica 10.2 behaves as if I'm supplying the wrong arguments. The "ID" you see there is not the Custom Search ID I created through Google's Custom Search Engine page. I tried to put the ID in manually as an argument, and I get the same result (well, lack of result).

Any help would be appreciated.

Thank you, Christian!

To my knowledge, dateRestrict allows one to request results from a specified number of past days/weeks/months.. I would be more interested in results within a date rage (of course you can run 2 requests and then take the complement, but life is too short to do this).

Another point, if I make a query with my name, I get a dozen of results from plus.google.com, which don't appear if I search that in Google.

To get the API Key you first have to go to https://console.developers.google.com and create a project if you don't have one yet. Once you have the project (asuming you are using the new console interface), click the Credentials menu at the left. There you'll see all your credentials. If don't have one, click the Add credentials and, for GoogleCustomSearch, you need the API key Browser key type.

For the Custom search engine ID, you have to go to https://cse.google.com/all and add a search engine. Once you create it, just click on that and you'll get a screen with a lot of options. There's a button there that says Search engine ID. Click it and you'll get the ID you need.

Regarding your original question, GoogleCustomSearch API supports the dateRestrict parameter, however, the WL connection does not support that parameter yet (but we have plans to add more support to this service).

Please let me know if you have questions about this functionality.

I have created a Google Custom search engine and from the site URL Basics tab can get the "Custom search engine ID" by clicking on its tab OK but cannot see how to get the "API key".

Help appreciated.

Did you get an Google Custom Search API key as per the manual:

https://reference.wolfram.com/language/ref/service/GoogleCustomSearch.html

You need at least version 10 to have ServiceExecute, I can't find when they introduced the GoogleCustomSearch, it might be 10.0 it might be 10.3. Which version of Mathematica are you using?

BTW - have you seen THIS?

results = ServiceExecute["GoogleCustomSearch", "Search", 
{"Query" -> "Orion spacecraft", "FileType" -> Except["png"], "MaxItems" -> 5, "SearchType" -> "Image"}]; 
results[All, {1, 2, 6, 7}]