There are chengyu with two numbers in them, for example:
一穷二白 (一, 二)
万众一心 (万, 一)
七上八下 (七, 八)
九五至尊 (九, 五)
But it seems that the selection of numbers is not completely random, and that certain numbers tend to have certain connotations.
My questions are:
I may answer to the first part of the question. I did a script to search all 4 characters ChengYu with your requirements. Here a resume about their number and the exaustive result from my db (ccdict).
一一(26)
一二(13)
一三(5)
一四(1)
一万(2)
一九(1)
一十(5)
二一(2)
二三(1)
二五(1)
二八(1)
二六(1)
二四(2)
三一(2)
三七(1)
三九(3)
三二(1)
三五(6)
三六(5)
三四(21)
四五(2)
四八(4)
五一(1)
五七(2)
五八(2)
五六(4)
五十(3)
五四(1)
六三(1)
六八(1)
六四(2)
七八(14)
七四(1)
八八(1)
九一(3)
九六(1)
十万(1)
十九(2)
十八(2)
十十(1)
万一(2)
万八(1)
Seems like 一一(26) , 三四(21) , 七八(14) , 一二(13) are the most common. Follows the complete (possibly not exhaustive) list.
一一(26)
一东一西
一丝一毫
一中一台
一举一动
一五一十
一分一毫
一唱一和
一夫一妻
一字一泪
一心一德
一心一意
一惊一乍
一房一厅
一朝一夕
一板一眼
一模一样
一步一趋
一点一滴
一点一点
一琴一鹤
一生一世
一瘸一拐
一言一动
一言一行
一递一个
一递一声
一万(2)
一本万利
以一驭万
一三(5)
一日三秋
一日三餐
一板三眼
一波三折
举一反三
一九(1)
一言九鼎
一二(13)
一干二净
一式二份
一心二用
一来二去
一清二楚
一清二白
一石二鸟
一穷二白
划一不二
数一数二
独一无二
臣一主二
说一不二
一十(5)
一暴十寒
一曝十寒
一目十行
假一赔十
闻一知十
一四(1)
一年四季
七八(14)
七七八八
七上八下
七嘴八张
七嘴八舌
七扭八歪
七拼八凑
七爷八爷
七老八十
七荤八素
七零八碎
七零八落
夹七夹八
杂七杂八
横七竖八
七四(1)
七政四余
万一(2)
万众一心
万无一失
万八(1)
万儿八千
三一(2)
三位一体
周三径一
三七(1)
三魂七魄
三九(3)
三教九流
三旬九食
三跪九叩
三二(1)
三心二意
三五(6)
三令五申
三侠五义
三番五次
三皇五帝
三纲五常
隔三差五
三六(5)
三亲六故
三十六计
三头六臂
三姑六婆
三茶六饭
三四(21)
三从四德
三催四请
三朋四友
不三不四
丢三落四
传三过四
低三下四
再三再四
勾三搭四
巴三览四
张三李四
挑三拣四
挑三窝四
推三阻四
朝三暮四
横三竖四
狂三诈四
说三道四
调三窝四
连三并四
颠三倒四
九一(3)
九九归一
九死一生
九牛一毛
九六(1)
九声六调
二一(2)
二十一条
二十一点
二三(1)
接二连三
二五(1)
二十五史
二八(1)
二十八宿
二六(1)
二十六岁
二四(2)
二十四史
二十四孝
五一(1)
五七一代
五七(2)
五劳七伤
五痨七伤
五八(2)
五花八门
五行八作
五六(4)
五脏六腑
五颜六色
人五人六
吆五喝六
五十(3)
一五一十
五代十国
五光十色
五四(1)
五湖四海
八八(1)
八荣八耻
六三(1)
六韬三略
六八(1)
六合八法
六四(2)
六十四万
六十四卦
十万(1)
六十四万
十九(2)
十成九稳
十拿九稳
十八(2)
十之八九
十有八九
十十(1)
十全十美
四五(2)
四分五裂
四舍五入
四八(4)
四平八稳
四通八达
四邻八舍
四面八方
I've come across a PhD dissertation which covers this exact topic plus many others:
Nall, Timothy M.
2009
It turns out this subject is much larger than I anticipated, so I'll only strictly answer the question I've asked (chengyu with only two numbers, patterns/meanings) and leave the rest for future questions.
The thesis concludes that there definitely are many patterns in chengyu with numbers, although exceptions exist because it is language after all. Numbers also tend to be used for the same meaning, influenced by schools of thought (yin yang), ancient literature (i-ching), and natural phenomena.
Within the two-number chengyu however, although there are structural patterns and in certain types of combinations, the specific numbers used are mostly arbitrary. The only exception is the seven/eight combination, used to mean "disorder".
Structural patterns
Out of 1895 chengyu with numbers (and number-like characters such as 半), 700 (or 37%) had two numbers. Of these:
# X # X (e.g. 一穷二白)X # X # (e.g. 朝三暮四)X X # #The popularity of certain forms, especially the # X # X form, is evidence that the thesis uses to support the idea that the selection of numbers is not entirely random, that there are cultural reasons for using certain numbers in certain ways. The rhythm of the chengyu is probably a major reason for the "interspersed" forms i.e. # X # X and X # X #, where the first pair of characters "balance" the second pair. The thesis cites many papers noting the prevalence of such parallelism in Chinese, especially classical and literary.
Number patterns
Number combinations
There's not too much information on special two-number combinations. The seven/eight combo seems to be an exception in this regard.
The thesis notes the influence of Yin Yang thought, where it's preferable to have a balance of Yin and Yang in chengyu. Odd numbers were attributed to Yang, and even numbers to Yin, and most chengyu with two different numbers (68%) have one Yin and one Yang number.
The seven/eight combination seems to have special meaning. Out of 37 chengyu with seven and eight, 29 are used to express disorder, untidiness or disturbance.
Apart from that, there seems to be no pairs that have special meaning. Instead, numbers can be used for various purposes, chosen arbitrarily:
Here are some pairs which frequently appear:
三 and 二/两: 三三两两, 三心二意, 三天两头, 三长两短. 三 and 五：三令五申, 三五成群, 三番五次, 三纲五常. 四 and 八：四平八稳, 四通八达. 三 and 六/九：三头六臂, 三六九等, 三教九流, 三公九卿, 三跪九叩. 五 and 十：五光十色, 一五一十. 千 and 百/万：千奇百怪、千方百计、千辛万苦、千恩万谢.You may notice that: (1) 三 is often used. In classical Chinese (文言文), 三 not only means the exact number of "three", but also "several". It's vague and thus widely used to describe several or some. (2) Very often, a number-pair consists of a number and its multiple (四 & 八, 五 & 十, 三, 六 & 九).
As a former Chinese elementary school student with rich experience of being forced into playing "name as many as possible chengyu with numbers!" games, I would say that in most cases, there are just no rules to follow. That's because, first, some chengyu are originated from historical stories or incidents, e.g. 过五关，斩六将 (from a story of Guan Yu. He literally went through five passes and killed six), 七擒七纵 (story of Zhuge Liang). These numbers are not changeable.
Second, there are just too many chengyu. Let's welcome 三 again: 举一反三, 三心二意, 三生三世, 朝三暮四, 三五成群, 三头六臂, 三七二十一, alas none with 八 (though there're 三八妇女节, and gossip woman, 三八), 三教九流.
It simply goes well with everyone.
BTW, though I didn't really enjoy the game mentioned above, it is good practice if you are interested in chengyu. You see, I can still recall loads of them without referring to dictionaries. :)
There's usually stories where the numbers come from. Can't remember a lot from when I learned them in grade school but here's one example.
九五至尊
至尊 means Supreme. It's usually associated with the emperor.
The nine and five, 九 and 五 respectively comes from the fact that nine is the largest single digit number and five is the middle number of the single digit numbers.
Here, the nine means grandest or biggest while five symbolizes the emperor to be the middle of everything.
As for others, there are stories behind why the numbers are used. I'll see if I can find the stories and link them here. BTW, always look at the 出处, which usually tells you where the chengyu is from and why it is that way.
Edit: 万众一心 (万, 一) - 万 is a large unit, meaning 10,000. 万众一心 means many people with one common goal. The reason they use 万 is probably because 万 is a big number at that time compared to 亿, the next biggest unit meaning 100 million.
Edit2: 一穷二白 is a made from a quote of Mao Zedong https://zh.wiktionary.org/zh/%E4%B8%80%E7%AA%AE%E4%BA%8C%E7%99%BD
It might be worth mentioning that early in the Three Character Classic it says the Five Elements 五行 come from numbers.
