Python 2.6, 886 - 1425 characters
My initial version (in the revisions) came in at 886 characters but did not satisfy the spec completely (it did not check for avoiding checkmate ; it didn't even consider the possible moves of the black pieces).
Now it does (and I've fixed several bugs in the original). Alas this comes with a cost in characters: 1425 for now, but there should still be little room for improvement. This version should be a lot more solid in handling edge cases then the previous one.
#-*-coding:utf8-*-
import sys;e=enumerate
B,W=["♟","♜","♞","♝","♛","♚"],["♙","♖","♘","♗","♕","♔"]
R={"♙":[11,42],"♖":[28],"♘":[31],"♗":[8],"♕":[8,28],"♔":[1,21]}
def F(w):return sum([[(i,j)for j,p in e(o)if p==w]for i,o in e(Z)],[])
def G(x,y):
P=Z[x][y];D=P in W;L=[]
for o in R[P]if D else R[unichr(ord(P.decode('utf8'))-6).encode('utf8')]:
r,k="%02d"%o
for g,h in[[(-1,-1),(1,1),(-1,1),(1,-1)],[[(1,-1),(1,1)],[(-1,-1),(-1,1)]][D],[(-1,0),(1,0),(0,-1),(0,1)],[(-2,-1),(-2,1),(-1,-2),(-1,2),(1,-2),(1,2),(2,-1),(2,1)],[(-1,0)]][int(r)]:
J=0
for i in range(int(k)):
T=x+(i+1)*g;U=y+(i+1)*h
if T<0 or T>7 or U<0 or U>7:break
M=Z[T][U]
if not J:L.append((T,U,P,M))
else:break
if r in"02"and(M in W+B):
J=1
if not((D and M in B)or(not D and M in W)):L.pop()
elif(r=="1"and not((D and M in B)or(not D and M in W)))or(r=="4"and((i==1 and x!=6)or M!="…")):L.pop()
return L
Z=[[y for y in l[5:].split()]for l in sys.stdin.readlines()[:-2]]
Q=[]
for p in R:
for i,j in F(p):
for M,L,c,_ in G(i,j):
O=Z[M][L];Z[i][j]="…";Z[M][L]=c;E=[];map(E.extend,map(F,B))
if not any(any(1 for _,_,_,I in G(v,h)if I==["♔","♚"][c in B])for v,h in E):Q.append((i,j,M,L,c))
Z[i][j]=c;Z[M][L]=O
(x,y,X,Y,p)=Q[0];Z[x][y]="…";Z[X][Y]=p
for i,h in e(Z):print`8-i`+' ║'+' '.join(h)
print"——╚"+"═"*16+"\n—— a b c d e f g h"
Example input and output:
# INPUT
8 ║♜ ♞ ♝ … ♚ ♝ ♞ ♜
7 ║♟ ♟ ♟ ♟ … ♟ ♟ ♟
6 ║… … … … … … … …
5 ║… … … … ♟ … … …
4 ║… … … … … … ♙ ♛
3 ║… … … … … ♙ … …
2 ║♙ ♙ ♙ ♙ ♙ … ♙ …
1 ║♖ ♘ ♗ ♕ ♔ ♗ ♘ ♖
——╚═══════════════
—— a b c d e f g h
# OUTPUT
8 ║♜ ♞ ♝ … ♚ ♝ ♞ ♜
7 ║♟ ♟ ♟ ♟ … ♟ ♟ ♟
6 ║… … … … … … … …
5 ║… … … … ♟ … … …
4 ║… … … … … … ♙ ♛
3 ║… … … … … ♙ ♙ …
2 ║♙ ♙ ♙ ♙ ♙ … … …
1 ║♖ ♘ ♗ ♕ ♔ ♗ ♘ ♖
——╚════════════════
—— a b c d e f g h