Python 2, 97 96 90 84 bytes

def f(s,c):r=range(len(s));return[c.join(c*i+s[:i:-1]+s[i:]+c*i)for i in r[:0:-1]+r]

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05AB1E, 15 11 bytes

.sûsζøsýí€û

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or as a Test Suite

Explanation

.s # push suffixes of input
 û # palendromize this list
 sζ # transpose using the second input as filler
 ø # transpose back
 sý # merge each on the second input
 í # reverse each row
 €û # palendromize each row

R, 118 bytes

function(a,d,n=length(a))for(i in c(n:1,1:n)[-n])cat(z<-rep(d,2*i-2),paste(c(a[n:i],a[0:-i]),collapse=d),z,'
',sep='')

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Thanks to Giuseppe for locating and fixing an error.

Japt, 15 bytes

Returns an array of lines

Ôå+ ®¬qV êÃûV ê

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Ôå+ ®¬qV êÃûV ê :Implicit input of strings U=s & V=c
Ô :Reverse U
 å+ :Prefixes
 ® :Map
 ¬ : Split
 qV : Join with V
 ê : Palindromise
 Ã :End map
 ûV :Centre pad each string with V, to the length of the longest
 ê :Palindromise

Charcoal, 15 bytes

ＵＢηＥθ✂θκ‖Ｏ↑←ＵＥ¹

Try it online! Link is to verbose version of code. Originally submitted as a comment on the now deleted sandbox post. Explanation:

ＵＢη

Set the background to the second input c.

Ｅθ✂θκ

Map over the first input s to generate all suffixes and implicitly print them on separate lines.

‖Ｏ↑←

Reflect horizontally and vertically.

ＵＥ¹

Add extra space horizontally.

J, 59 56 bytes

,~[:((0-2*#).[:,0,:"0(:>:t)*t=:]+/<:)[:(.,])#@]

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Too long solution for J ... (entirely my fault)

R, an ugly 118 bytes version

By letting the input be a vector of single characters, and outputting a matrix instead of printing nice ascii art.

function(s,C,l=length(s),L=4*l-3,k=2*l-1,y=abs(rep(1:k,L)-l)+abs(rep(1:L,e=k)-k)/2+1)matrix(ifelse(y%%1|y>l,C,s[y]),k)

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R, 161 157 bytes

saved 4 bytes by using ifelse instead of conditionally modifying y

function(S,C,l=nchar(S),L=4*l-3,k=2*l-1,y=abs(rep(1:L,k)-k)/2+abs(rep(1:k,e=L)-l)+1)cat(rbind(matrix(ifelse(y%%1|y>l,C,el(strsplit(S,''))[y]),L),'
'),sep='')

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ungolfed and commented

function(S,C)
 s=el(strsplit(S,''))
 l=nchar(S)
 L=4*l-3
 k=2*l-1
 y=abs(rep(1:L,k)-k)/2+abs(rep(1:k,e=L)-l)+1 # distance from centre
 y[!!y%%1]=l+1 # set non integers to one more than length of string
 y[y>l]=l+1 # set number beyond length of string to one more than length of string
 M = rbind(matrix(c(s,C)[y],L),'n') # build matrix and add line returns
 cat(M,sep='') # print the matrix as a string

hmmm, seems like the longest answer so far!

Wolfram Language (Mathematica), 121 bytes

Join[q=Table[(v=Table[#2,2(l-k)])<>Riffle[Join[(h=Reverse)[n=(g=Take)[#,-k]],g[n,-k+1]],#2]<>v,k,l=Length@#],Rest@h@q]&

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Japt, 16 bytes

Note: I'll golf it :)

Ôå+ ®¬qVÃùV mê ê

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PowerShell, 120 bytes

param($s,$c)($s,(($l=$s.length-1)..0+1..$l|%($x=$c*(2*$_))+($s[($_,($l..$_+($_+1)..$l))[$_-ne$l]]-join$c)+$x))[$l-gt0]

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Some days, having index ranges instead of slices really hurts. Today is one of those days. Due to conjoined ranges messing up when dealing with single elements (e.g. returning 0..0+1..0), special-casing is used to avoid it altogether (at the cost of many bytes).

Jelly, 11 bytes

jÐƤṚzṚŒḄZŒḄ

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Left argument: $s$.

Right argument: $c$ (as a single character, not as a string).

Output: List of Jelly strings (appears as a list of lists of 1-char Python strings, replace ŒṘ with Y to see the n-joined output).

PowerShell, 82 83 bytes

+2 bytes thanks Veskah: the single character case bug fixed

-1 byte: The rule Input-string may also be a list of characters used

$c,$s=$args
($s|%(-join$s)[($r=$i..0+1..$i)]|%"$_"[$r]-join$c

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Less golfed:

$c,$s=$args
$southEast = $s|%% substring $i) + $c*$i++

$range=$i..0+1..$i
$southEast[$range]|%
 "$_"[$range]-join$c

Ruby, 95 84 75 bytes

->a,c(1...2*z=a.size).map

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Takes input string as an array of chars. Returns an array of strings.

Japt, 15 bytes

Ôå+ ê ®ê ¬qV
ûV

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Perl 5 with -lF, -M5.010, 71 bytes

$"=<>;$A=abs,$_="@F[$A..$#F]".$"x($A*2),/./,say reverse.$' for-$#F..$#F

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Pip, 24 20 bytes

QPRV:_JbMa@>RV,#aZDb

Use the -l flag to get human-readable output. Try it online!

Explanation

QPRV:_JbMa@>RV,#aZDb
 a,b are cmdline args (implicit)
 a 1st cmdline arg (the string)
 # Length
 , Range
 RV Reverse
 a@> Take slices of a starting at those indices
 ZDb Zip the list of slices together, filling out missing values in
 the matrix with b (the character)
 M To each row, map this function:
 _Jb Join on b
 RV: Reverse (making top row the bottom and vice versa)
QP Quad-palindromize: reflect downward and rightward, with overlap

For example, with inputs of abcd and .:

RV,#a
 [3 2 1 0]
a@>
 ["d" "cd" "bcd" "abcd"]
ZDb
 [['d 'c 'b 'a] ['. 'd 'c 'b] ['. '. 'd 'c] ['. '. '. 'd]]
_JbM
 ["d.c.b.a" "..d.c.b" "....d.c" "......d"]
RV:
 ["......d" "....d.c" "..d.c.b" "d.c.b.a"]
QP
 ["......d......" "....d.c.d...." "..d.c.b.c.d.." "d.c.b.a.b.c.d" "..d.c.b.c.d.." "....d.c.d...." "......d......"]

C# (Visual C# Interactive Compiler), 249 bytes

s=>c=>var r=s.Select((x,_)=>int k=s.Length;var m=s.Substring(_,k-_).Aggregate("",(a,b)=>a+c+b);return new string(m.Skip(2).Reverse().Concat(m.Skip(1)).ToArray()).PadLeft(2*k-3+m.Length,c).PadRight(4*k-3,c););return r.Skip(1).Reverse().Concat(r);

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This must be improvable...

K (ngn/k), 38 bytes

x

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Canvas, 8 bytes

Ｒ±［］／┼┼＊

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7 bytes but mirrors a bunch of chars.

TSQL query, 200 bytes

In MS-SQL Server Management Studio press Ctrl-T before running this query, this will change the output to text.

This script is building up the output from left to right in one long "string", calculating the value to put in each position, output starts with a line-break. The output is limited to 4096 characters.

Golfed:

USE master
DECLARE 
@y char='.',
@ varchar(20) = 'abcd'

SELECT
string_agg(iif(h>k/2,@y,substring(@,h+1,1),@y)+iif((n+1)%k=0,char(13)),'')FROM(SELECT
abs(k/2-n%k)+abs(k/2-n/k)h,*FROM(SELECT
number n,len(@)*2-1k,*FROM spt_values)c)d
WHERE n<k*k and'P'=type

Ungolfed:

USE master
DECLARE 
@y char='.',
@ varchar(32) = 'abcd'

SELECT 
 string_agg(iif(h>k/2,@y,substring(@,h+1,1))+iif((n+1)%k=0,char(13),@y),'')
FROM
 (
 SELECT abs(k/2-n%k)+abs(k/2-n/k)h,*
 FROM
 (
 SELECT number n,len(@)*2-1k,*
 FROM spt_values
 )c
 WHERE n<k*k and'P'=type
 )d

I had to make some changes to format the output in the online version.

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JavaScript (Node.js), 143 bytes

(s,c)=>q=Math.abs;m=(l=s.length*4-3)-1;for(i=j=0;j<l/2;(i=(++i)%l)?0:++j)p=s[q(i-m/2)/2+q(j-m/4)];process.stdout.write((i?"":"n")+(p?
p:c))

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A bit more thinkering would lead to calculating in terms of a one-dimensional array, and less bytes.

Perl 6, 79 bytes

->cmap ,g .[^*X+(^$_,)]o*.comb
my&g=.[$_-1...0...$_-1]

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Anonymous codeblock that takes input curried (like f(char)(string)) and returns a list of strings. I think a different approach would be shorter.