Stefandk
What you have is a typical EMI/EMC type issue. The MSC1210 is an A/D w/8051 core and the ADS1240 is the A/D as a separate peripheral. Obviously, to exercise two different parts, you have two different layouts.
Solving and EMC type issue without using brute force (i.e. shielded box with all shielded I/O) requires careful attention to detail. To stop EMI, you must do one or more of the following:
I) Keep the RF from getting to your circuit - shielded enclosure, shields over sensitive parts of the circuit, multilayer boards with external ground and internal signal routing.
II) shunt the RF being impressed on a possible sensitive trace to ground with a low impedance path for the RF (translation - a small capacitor to ground with minimum connection inductance).
III) Stop an RF signal from traveling along a wire connection or long trace by creating a high impedance for the RF so it doesn't want to travel the wire (translation - ferrite bead, series inductor, or sometime just a series resistance).
What to do:
1) Careful examination of the layout you have A)how long traces are to high impedance points, B) good continuous ground with a minimum slots or notches which provides a low impedance at high frequencies,
2) Proper bypassing at power pins (more than one capacitor with one or two decades of value difference paralleled at VCC with short connections from VCC to ground - i.e. a 0.1uF and a 1nf in parallel. Remember - connection length is equivalent to inductance, and inductance along with capacitance forms a resonant circuit.
3) Proper bypassing at analog signal pins - especially if they are high impedance. Again bypass close to the input pin of the A/D with short connections to ground. Sometimes just 33pf to 120pf is all you need to provide a low impedance path to ground for any RF signal. Be sure to do this at your analog input pins, reference pins, and other pins where the small capacitance will not interfere with the operation of your device.
4) Use one or more ferrite beads over the leads to your load cell at the point where they connect to the board.