I did this for fun - I'd love to find a 1983 2p with the 'New Pence' reverse, or any NCLT 2p for that matter. And I'm still waiting for my first 2017 2p - it has a mintage of 16,600,000 but I've yet to see one in circulation!
So here are the results!
1971 85
1975 23
1976 2
1977 9
1978 13
1979 13
1980 30
1981 21
1985 11
1986 16
1987 24
1988 34
1989 34
1990 18
1991 6
1992 9
1993 21
1994 40
1995 5
1996 28
1997 50
1998 bronze 12
1998 copper clad steel 6
1999 36
2000 41
2001 53
2002 16
2003 32
2004 36
2005 27
2006 17
2007 32
2008 Ironside 1
2008 shield 29
2009 23
2010 12
2011 16
2012 21
2013 8
2014 39
2015 Rank-Broadley 9
2015 Jody Clark 24
2016 Jody Clark 17
OTHER COINS
Jersey 1992 1
Bronze total 351
Copper plated steel total 649
TOTAL: 1,000

Despite some of the outrageous prices you see on
ebay, the original design of 2p coin issued in 1971 and from 1975 to 1981 is still exceedingly common: indeed 1971 is still the commonest date of 2p coin in circulation! It's strange how scarce 1976 coins are: I remember trying to find one for a Spanish collector about 20 years ago and it took me ages to get one, although
The Royal Mint website gives the mintage as 181,379,000 - higher than the mintage figure for 1975!

All Maklouf portrait coins from 1985 to 1997 are plentiful.

The Rank-Broadley coins issued from 1998 to 2008 are common with the exception of the 2008 coin with the Ironside reverse, which has a mintage of only 10,600,000. I find the bronze 1998 2p commoner than the steel version, although according to the official mintage figures it should be the other way around!

Shield reverse coins are getting commoner. 2016-dated 2p coins were very scarce in 2016-7, but are much easier to find now, though I suspect not all the mintage of 185,600,000 have been released. I have still not seen a 2017 2p...