In 1871, there were in order of succession:
1. Wilhelm I. (regnant)
2. Friedrich (III.), Son of 1
3. Wilhelm (II.), Son of 2
4. Heinrich, Son of 2
5. Waldemar, Son of 2
6. Carl, Brother of 1
7. Friedrich Karl, Son of 6
8. Friedrich Leopold, Son of 7
9. Albrecht (until 1872), Brother of 1
10. Albrecht, Son of 9
11. Alexander, Great-Grandson of King Wilhelms Grandfather FW III
12. Georg, Great-Grandson of King Wilhelms Grandfather FW III
(By 1880, 10 will have three sons.)
That is quite a massacre.
They might to jump to the Swabian branch, whose head in 1871 is
Sw1. Prince Karl Anton (dies 1885)
Sw2. Leopold, Son of Sw1
Sw3. Wilhelm, Son of Sw2
Sw4. Ferdinand, Son of Sw2
Sw5. Karl Anton, Son of Sw2
Sw6. Karl, Son of Sw1
Sw7. Friedrich, Son of Sw1
If the 19 men above are all killed before they can have any issue, then a suspension of Salic Law in favor of a Pragmatic Sanction-style would point at the eldest daughter of the latest king. That would be (in 1871) King Wilhelm I.:
Princess Luise, since 1856 the Grand Duchess of Baden (wife of GD Friedrich I. of Baden)
If W1 predeceases his son Friedrich III., then the eldest daughter of the latest monarch will be
Princess Charlotte, born in 1860 and unmarried until OTL 1878 (but engaged to Prince Bernhard of Saxe-Meinigen since 1876)
In 1871, 3, 4 and 5 have no daughters,
6 has two daughters, both married to mediatized Landgraves of Hesse,
7 has Pss Marie, after 1878 married to Prins Hendrik of the Netherlands,
8 has no daughters,
9 has as eldest surviving daughter Pss Alexandrina. Since 1865 married to Duke Wilhelm of Mecklenburg, younger brother of the ruling Grand Duke of M-Schwerin. He was notorious as gambler, generally considered to be the "black sheep" of the family. The Berlin Court gave him the nickname "Prinz Schnaps" - "Prince Booze".