Solution #1: Using Math formula and MODEL clause:

WITH m AS (  
SELECT 63 AS cents  
FROM dual   
)  
SELECT cents "Change",   
       Q "Quarters",   
       D "Dimes",   
       N "Nickels",   
       P "Pennies"  
FROM m  
MODEL  
DIMENSION BY(0 AS dummy)  
MEASURES(  
 cents,  
 CAST(0 AS NUMBER(3)) AS Q,  
 CAST(0 AS NUMBER(3)) AS D,  
 CAST(0 AS NUMBER(3)) AS N,  
 CAST(0 AS NUMBER(3)) AS P  
)  
RULES (  
 Q[0]=FLOOR(CENTS[0]/25),  
 D[0]=FLOOR((CENTS[0]-Q[0]*25)/10),  
 N[0]=FLOOR((CENTS[0]-Q[0]*25-D[0]*10)/5),  
 P[0]=(CENTS[0]-Q[0]*25-D[0]*10-N[0]*5)  
)

Solution #1a: Using Math formula and MODEL clause - for all change values between 1 and 99

WITH m AS ( 
SELECT LEVEL cents 
FROM dual  
CONNECT BY LEVEL<=99 
) 
SELECT cents "Change",  
       Q "Quarters",  
       D "Dimes",  
       N "Nickels",  
       P "Pennies" 
FROM m 
MODEL 
PARTITION BY(ROWNUM AS rn) 
DIMENSION BY(0 AS dummy) 
MEASURES( 
 cents, 
 CAST(0 AS NUMBER(3)) AS Q, 
 CAST(0 AS NUMBER(3)) AS D, 
 CAST(0 AS NUMBER(3)) AS N, 
 CAST(0 AS NUMBER(3)) AS P 
) 
RULES ( 
 Q[0]=FLOOR(CENTS[0]/25), 
 D[0]=FLOOR((CENTS[0]-Q[0]*25)/10), 
 N[0]=FLOOR((CENTS[0]-Q[0]*25-D[0]*10)/5), 
 P[0]=(CENTS[0]-Q[0]*25-D[0]*10-N[0]*5) 
) 
ORDER BY 1

Solution #2: Using Enhanced Math formula

WITH a AS (  
SELECT 63 cents  
FROM dual  
)  
SELECT a.cents "Change",  
       FLOOR(a.cents/25) "Quarters",   
       FLOOR(MOD(a.cents,25)/10) "Dimes",  
       FLOOR(MOD(MOD(a.cents,25),10)/5) "Nickels",  
       MOD(MOD(MOD(a.cents,25),10),5) "Pennies"  
FROM a

Solution #2a: Using Enhanced Math formula - for all change amount between 1 and 99

WITH a AS (  
SELECT LEVEL cents  
FROM dual  
CONNECT BY LEVEL<100  
)  
SELECT a.cents "Change",  
       FLOOR(a.cents/25) "Quarters",   
       FLOOR(MOD(a.cents,25)/10) "Dimes",  
       FLOOR(MOD(MOD(a.cents,25),10)/5) "Nickels",  
       MOD(MOD(MOD(a.cents,25),10),5) "Pennies"  
FROM a  
ORDER BY a.cents

Solution #3: Using Cartesian Product and Top Record pattern approach

WITH r AS (  
SELECT LEVEL-1 n  
FROM dual  
CONNECT BY LEVEL<=20  
), x AS (  
SELECT q.n "Quarters", d.n "Dimes", n.n "Nickels", p.n "Pennies",  
 RANK() OVER(ORDER BY q.n + d.n + n.n + p.n) rk  
FROM r q, r d, r n, r p  
WHERE q.n<=3  
 AND d.n<=9  
 AND n.n<=19 --not really needed  
 AND p.n<=4  
 AND q.n*25 + d.n*10 + n.n*5 + p.n = 63 --amount of change  
)  
SELECT "Quarters", "Dimes", "Nickels", "Pennies"  
FROM x  
WHERE rk=1

Solution #3a: Using Cartesian Product and Top Record pattern approach - for all change amounts between 1 and 99 cents

WITH r AS ( -- this range is to be reused 5 times in this query  
SELECT LEVEL-1 n  
FROM dual  
CONNECT BY LEVEL<=100  
), x AS (  
SELECT c.n "Change", q.n "Quarters", d.n "Dimes",   
       n.n "Nickels", p.n "Pennies",  
       RANK() OVER(PARTITION BY c.n ORDER BY q.n + d.n + n.n + p.n) rk  
FROM r q, r d, r n, r p, r c  
WHERE q.n<=3  
 AND d.n<=9  
 AND n.n<=19 --now it is needed  
 AND p.n<=4  AND q.n*25 + d.n*10 + n.n*5 + p.n = c.n --amount of change    
 AND c.n>0  
)  
SELECT "Change", "Quarters", "Dimes", "Nickels", "Pennies"  
FROM x  
WHERE rk=1  
ORDER BY 1