Tyranitar is in the Monster Egg Group.
The Pokemon families in this group are;
Bulbasaur
Charmander
Nidoran (male)
Nidoran (female)*
Slowpoke
Cubone
Lickitung
Rhyhorn
Kanghaskan
Lapras
Snorlax
Chikorita
Totodile
Mareep
Larvitar
Treeko
Mudkip
Whishmur
Aron
Tropius
Turtwig
Cranidos
Shieldon
Gible
Snowver
Axew
Drudiggon
Ditto
Note that all evolutions of these Pokemon are also in the Monster Egg Group but not always pre-evolutions.
Pokemon marked with * are exceptions. Their evolutions are not in the Monster Egg Group.
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Eevee's egg group is Field.
Clefairy's Egg Group is Fairy, so any Pokemon with the same Egg Group can breed with Clefairy, including Ditto, which has its own Egg Group.
Tyranitar
Rotom is in the Amorphus egg group, so it can breed with any Pokemon in that egg group.
jigglypuff and ditto can and will have an egg if left in daycare for long enough. only legendary Pokemon and Pokemon in the -no egg- group will not produce an egg...being in the fairy egg group, jigglypuff will produce an egg