Is there a way to add a record (using a formula button in a report) without being redirected to that record?

Do you want to refresh the report / record you are on or just have a quiet fade away pop up saying that the record has been added?

Here is an example.  You will need to disable the need for app tokens or else add a line to the code like

& "&apptoken=xxxxxxxxxx"

var datetime SnoozeUntil = ToTimestamp(Today() + Days(1), ToTimeOfDay("0:00"));


var text URL = URLRoot() & "db/" & [_DBID_DEALLOCATION_CANDIDATES] & "?act=API_EditRecord"
 & "&rid=" & [Record ID#]
 & "&apptoken=xxxxxxxxxx"
 & "&_fid_415=" & ToText($SnoozeUntil)
 & "&_fid_416=" & ToText(Now()); // set the date/time so we know if the line existed when snoozed


 
"javascript:" &
"$.get('" & 
$url & 
"',function(){" &
"$.jGrowl('put your pop up words here', {life: 5000, theme: 'jGrowl-green'});" &
"});" &
"void(0);

I get an error for [_DBID_DEALLOCATION_CANDIDATES]  what is that supposed to refer to?

Also, the popup is not necessary

You will want to let the user know that clicking the button "worked' or else they will just keep on clicking it and lot of child records will be created.  In any event, the pop up does not slow down the process.   The 5000 means 5 seconds before the pop up fades away on its own.  You can adjust that as you like.

I see what you are saying, thanks. Now the popup is working and it creates the record in IRR but the record is not connected to the ticker (parent record)
This is what I have:

var datetime SnoozeUntil = ToTimestamp(Today() + Days(1), ToTimeOfDay("0:00"));


var text URL = URLRoot() & "db/" & [_DBID_IRR] & "?act=API_AddRecord"
 & "&rid=" & [Record ID#]
 & "&apptoken=qqj2k7wz..."
 & "&_fid_415=" & ToText($SnoozeUntil)
 & "&_fid_416=" & ToText(Now()); // set the date/time so we know if the line existed when snoozed


 
"javascript:" &
"$.get('" & 
$url & 
"',function(){" &
"$.jGrowl('Record Added', {life: 5000, theme: 'jGrowl-green'});" &
"});" &
"void(0);

I got It! 
var text URL = URLRoot() & "db/" & [_DBID_IRR] & "?act=API_AddRecord"
 & "&_fid_10=" & URLEncode([Record ID#])

Thanks for your help!

OK, so you are not understanding my example,

a line like this 

& "&_fid_416=" & ToText(Now())

means to populate fid 416 with a value.

so similar to your original formula
 you need to put in a line like 

&_fid_10=" & URLEncode ([Record ID#])


to connect the child to the Parent because your field 10 is the field for [Related Parent]