My baby son likes peaches, plums, apricots and nectarines.  What’s the name of this group?

While they may not be genetically related, I think the word you are looking for is drupaceous.

Looking up ‘stone’ I found:

3a b : the hard central portion of a drupaceous fruit (as a peach) c : a hard stony seed (as of a date)

and "drupacious" yields:

1 : of or relating to a drupe
2 : bearing drupes

so we move on through these seemingly circular references to "drupe" to finally find:

Etymology: New Latin drupa, from Latin, overripe olive, from Greek dryppa olive
Date: circa 1753
: a one-seeded indehiscent fruit having a hard bony endocarp, a fleshy mesocarp, and a thin exocarp that is flexible (as in the cherry) or dry and almost leathery (as in the almond)

"Indehiscent" means "remaining closed at maturity," which sounds like some minds I know.  Endocarp, mesocarp, and exocarp have nothing to do with Koi and their ilk, however.  

Endocarp:  Etymology: French endocarpe
Date: 1830
: the inner layer of the pericarp of a fruit (as an apple or orange) when it consists of two or more layers of different texture or consistency

Pericarp:  Etymology: New Latin pericarpium, from Greek perikarpion pod, from peri- + -karpion -carp
Date: 1759
: the ripened and variously modified walls of a plant ovary

Mesocarp:  the middle layer of a pericarp

Exocarp:  the outermost layer of the pericarp of a fruit

and finally:

end-
Function: combining form
Etymology: French, from Greek, from endon within; akin to Greek en in, Old Latin indu, Hittite andan within—more at IN
Variant(s): or endo-
1 : within : inside—compare ECT-, EXO-
2 : taking in

peri-
Function: prefix
Etymology: Latin, from Greek, around, in excess, from peri; akin to Greek peran to pass through—more at FARE
1 : all around : about
2 : near
3 : enclosing : surrounding

mes-
Function: combining form
Etymology: Latin, from Greek, from mesos—more at MID
Variant(s): or meso-
1 : mid : in the middle
2 : intermediate (as in size or type)

exo-
Function: combining form
Etymology: Greek exO out, outside, from ex out of—more at EX-
Variant(s): or ex-
1 : outside : outer—compare ECT-, END-
2 : turning out

-carp
Function: noun combining form
Etymology: New Latin -carpium, from Greek -karpion, from karpos
: part of a fruit : fruit

"Whew!"

Being simple folk here in New Zealand, we simply call them ‘stone fruit’.  :-[

I don’t know of a site that provides a complete taxonomy of the plant kingdom, but here’s an excellent one for critters:

http://animaldiversity.ummz.umich.edu/

Is there a word for just the 4 big stone fruit?  I’d have a hard time including olives!  But I’d also like to exclude cherries if possible.  Sorry to be so pernickety.

(Did I get that right?  I remember it’s not persnickety!)

I know that many pitted fruits belong to the genus punus, this however also included cherries and almonds, and would just be the same as using, as Linnet suggested, "stone fruit".

This is a list of common classifications for plant based foods
http://www.parentsofallergicchildren.org/biologic.htm

I’ll keep looking.

All the best,
Barnett

Thanks.  I’ll go with "large stone fruit" for now.  Cumbersome, but correct.

[quote author=tamisaac link=board=what;num=1030843261;start=0#6 date=09/02/02 at 16:36:27]Thanks.  I’ll go with "large stone fruit" for now.  Cumbersome, but correct.

I wondered if that shouldn’t be large stoned fruit then I realised that stoned has another meaning!  
But large-stoned fruit would be safe.
Bryn