They almost certainly had other children, but the number, ages, and genders are not consistent from census to census, which suggests there were some  individuals living with them who were not their children, so not much about their children can be securely deduced from the censuses.

1.  Marriage Record:

2.  Pennsylvania German Society.  1983.  "Birth and Baptismal Register of Trinity Lutheran Church, Lancaster, PA."  Pages 1-225 in Pennsylvania German Church Records. Genealogical Publ. Co., Baltimore, MD (Broderbund CD-130).

p. 143	1783... Georg. Kapp, s. Martin and Anna Maria; b. March 3; bap. April 21.
p. 157	1785... Daniel Kapp; s. Martin and Anna; b. May 30; bap. Sept. 7.
p. 170	1787... Elisabeth Kapp, d. Martin and Hanna; b. Oct. 19; bap. Nov. 25.
p. 181	1790... Johannes Kapp, s. Martin and Anna Maria; b. May 31; bap. August 1.

3.  1790 Census Index and Digital Images (online at Ancestry.com; Image #3 of 6; extracted by Diana Gale Matthiesen):

1790

PA

Lancaster Co.

Manheim Twp.

p. 145

Ln. 8

Martin Kopp

1-3-3-0-0

These data indicate:

Gender and Type	Age Class	Therefore Born	Individuals Inferred
1 free white male	16 or over	in or bef. 1774	= Martin
3 free white males	15 or under	1774-1790	= George (b. 1783) = Daniel (b. 1785) = Johannes (b. 1790)
3 free white females	all ages	in or bef. 1790	= Anna = Elizabeth (b. 1787) = ?

4a.  Census Index:  U.S. Selected Counties, 1800 (Broderbund CD-312).  Please see my WARNING regarding use of this database (the numerical data have the genders switched). 

1800

Sapp, Martin

PA

Lancaster Co.

p. 18

11010-2201000

How in the world this got misread as "Sapp" is beyond me.

4b.  1800 Census Index and Digital Images (online at Ancestry.com; Image #2 of 6; extracted by Diana Gale Matthiesen):

1800

PA

Lancaster Co.

Mountjoy Twp.

p. 18

Ln. 11

Martin Kapp

22010-11010-00

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	9 or under	1790-1800	= ? = ?
2 males	10-15	1784-1790	= Johannes (b. 1790) = Daniel (b. 1785)
1 male	26-44	1755-1774	= Martin
1 female	9 or under	1790-1800	= ?
1 female	10-15	1784-1790	= Elizabeth (b. 1787)
1 female	26-44	1755-1774	= Anna

5.  1810 Census Index and Digital Images (online at Ancestry.com; Image #5 of 5; extracted by Diana Gale Matthiesen):

1810

PA

Lancaster Co.

Mountjoy Twp.

p. 338/361

Ln. 11

Martin Kapp

01201-02101-00

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-15	1794-1800	= ?
2 males	16-25	1784-1794	= Johannes (b. 1790) = Daniel (b. 1785)
1 male	45 or over	in or bef. 1765	= Martin
2 females	10-15	1794-1800	= ? = ?
1 female	16-25	1784-1794	= Elizabeth (b. 1787)
1 female	45 or over	in or bef. 1765	= Anna Maria

6.  1820 Census Index and Digital Images (online at Ancestry.com; Image #2 of 6; extracted by Diana Gale Matthiesen):

1820

PA

Lancaster Co.

Mountjoy Twp.

p. 16/155

Ln. 13

Martin Capp

010101-02000-0-200

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-15	1804-1810	= ?
1 male	19-25*	1794-1801	= ?
1 male	45 or over	in or bef. 1775	= Martin
2 females	10-15	1804-1810	= ? = ?
2	persons engaged in agriculture
*In the 1820 Census, the third column is age class 16-18 and the fourth column is age class 16-25; therefore, any individual in column three is duplicated in column four.  By subtracting the number in column three from the number in column four, you can create an age class "19-25."

Anna has apparently died.

7.  1830 Census Index and Digital Images (online at Ancestry.com; Image #5 of 28 — indexed "Copp"; extracted by Diana Gale Matthiesen):

1830

PA

Lancaster Co.

Mount Joy Twp.

p. 96

Ln. 16

Martin Capp

101 001 000 100 - 001 110 000 000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1825-1830	=
1 male	10-14	1815-1820	=
1 male	30-39	1790-1800	=
1 male	70-79	1750-1760	= Martin
1 female	10-14	1815-1820	=
1 female	15-19	1810-1815	=
1 female	20-29	1800-1810	=

It's hard to say, at this point, just who is living with Martin, probably some children and grandchildren, plus possibly some hired help.  Martin is listed one line above Mary CAPP (000 000 000 - 000 101 100).

8a.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):  not found.

8b.  1840 Census Index and Digital Images (online at Ancestry.com):  not found, and I checked every page of Mount Joy Twp.

9.  Messages in the Kapp Family Genealogy Forum (online at GenForum.com).

10.  U.S. Geological Survey.  GNIS:  Geographic Names Information Service (online database).  The GNIS says, "Mount Joy," but clearly the locals historically knew it as Mountjoy.  Mount Joy is a mountain; Mountjoy is an English surname.  Does anyone know for what/whom the town and township were originally named?  In checking a topo map, there is no mountain anywhere near Mount Joy.  There is a Mt. Joy in Pennsylvania, but it's in Montgomery Co., nearer to Philadelphia than it is to Lancaster.