Can the Tailed Beasts produce offsprings? Is it possible for the Tailed Beasts to produce offspring of their own? Both 'male' and 'female' type Tailed Beasts exist. 

The offspring would be hybrid, but still, would it be possible?
There is no canon answer to your question. The tailed beasts as they currently exist in the Narutoverse are chakra creatures, not biological, and came into existence because one entity (the 10 Tails) had its chakra separated from its body (which became the Moon), which was then artificially split into a number of separate beings. There is no indication that any of these creatures (or chakra based entities in general) can reproduce themselves in any way similar to organic sexual reproduction. 

If you're asking about the kitsune as a concept in actual Japanese folklore (which is the basis for Kishimoto's tailed beasts), then the answer is: the kitsune are considered a type of yokai or kami, who can if powerful and wise enough, take the form of a human being (usually but not limited to a beautiful woman). There are many stories of foxes in the guise of a beautiful woman falling in love with and marrying a human and producing offspring.

The real-life Sengoku general Takeda Shingon's wife Suwa Koi was believed to be a malevolent fox-spirit, and she bore him Takeda Katsuyori. Abe no Seimei in the Heian period was also considered a child of a fox.

Sources: 


Ashkenazy, Michael "Handbook of Japanese Mythology." 2003.
Hearn, Lafcadio "Glimpses of Unfamiliar Japan." 2005.
Turnbull, Stephen. "Nagashino 1575." 2000.