My husband and I are determined to have our first son have the nickname Bif, but we couldn’t find any names with Bif as a nickname. Any suggestions? (Preferably with Bif at the beginning of the name) 
The only one that comes to mind is Biford/Byford
I feel honorbound to mention the less than stellar cultural allusions to [name_m]Biff[/name_m] (Back to the [name_u]Future[/name_u] and Death of a Salesman), but they probably don’t bother everyone.
My first thought was to find a name that started with Bi-/By- and then pair it with a middle name that starts with F. But there are limited Bi/By names:
[name_m]Bingham[/name_m]
[name_m]Birch[/name_m]
[name_m]Birke[/name_m]
[name_m]Bishop[/name_m]
[name_m]Byron[/name_m]
Of these, I like [name_m]Bishop[/name_m] and [name_m]Byron[/name_m]. [name_m]Bishop[/name_m] [name_m]Fox[/name_m], [name_m]Byron[/name_m] [name_m]Frederick[/name_m], [name_m]Byron[/name_m] [name_m]Fraser[/name_m], etc.
My other suggestion is that rather than contorting names that you may not like to suit a nickname, just name him what you want and call him Bif. Bif seems like one of those all around nicknames like [name_m]Buck[/name_m], [name_m]Duke[/name_m], [name_m]Buddy[/name_m], [name_m]Bubba[/name_m], etc that aren’t tied to a specific name. I have a brother, an uncle, a cousin, and an aunt who have always gone by nicknames that have nothing to do with their first names, so it doesn’t seem strange to me.
I think you’d have slightly less resistance if his first name started with a B, but people will generally call him what you call him.
I can only have negative thoughts on this name. [name_m]Buford[/name_m] is the only longer form I can think of.
Agree with this. Bif (or [name_m]Biff[/name_m]) would work fine as a nickname for just about anything, I think.