Hi,
Child phones ate simplest cellphones you could design , cost however depends on the design complexity.
1. Many companies like SIMCOM offers low cost GSM modem chips that could be used in such cellphones. (SIM900 may be the choice)
2. Complicated part is battery, as Lithium Ion batteries are dangerous when it comes to charging them. You need to have knowledge of basic power circuitry. National Semi, Maxim , Analog Devices supplies battery charger IC, application notes may be useful from them.
3. Antennas can be bought ready made as most companies do.
4. Now about the controller, it depends what features you want in.
a. For basic design with only keypad and mic/headphone as simple 8051 (variants from NXP, Atmel, Dallas Semi) may do the job. As you go further to add simple LCD, still it's worth to use 8051.
b. If you wanna add more functionality like battery management, signal strength monitoring, graphical displays, go for AVR of PIC (variants are available easily)
c. If you wish to go for cool basic level phone ARM7 ARM9 (NXP ,ST Micro,ATMEL) and variants can be used, you may add color and touch based displays then.
5. Regarding PCB designing, a local PCB house may help you getting PCB quickly, provided you give them gerber files required, of simply offshore the job of circuit designing to someone and he will do that job, provided you decide the controller and GPIO mapping of the same to designer.
Happy designing
Regards
Atul Undre