Every date you enter for your ancestor’s life needs to have a source. That includes dates that are estimated.
If you are using the fact that a man got married without permission on 2 June 1891 when the age for a man in that location to get married without permission was twenty-one as evidence for his date of birth, then indicate that. In this case, you should state he was born before 3 June 1870, cite the marriage record (and in your notes explain the age requirement and the fact that no permission was given–it might even be a good idea to read quite a few other records besides those of the ancestor to see if any of them do have permission notated).
If you are using an ancestor’s 1850 census enumeration as their “last known alive date” cite that census for the “dead after” date and in your notes indicate what searches of other records have been conducted.
Never indicate a date is exact when it is not. Often in genealogical research we know an event took place before or after a certain date. Cite your source(s) and in your notes explain–particularly if the reasoning may not be obvious to someone else (or even to you later).