The MAX1757/MAX1758 with internal MOSFETS and the MAX1737 that drives external MOSFETs share a lot of internal circuitry. One feature that the devices have in common is that they measure the battery pack thermistor voltage periodically. As this measurement is a precision measuement, and the thermistor ground is normally in common with the battery pack ground terminal, the battery charger stops charging during the measurement of the thermistor to avoid any ground return voltage bounce. This results in a "quiet" period to sample the temperature.
This is documented in the MAX1737 electrical characteristics table, page 4:
Temperature Measurement Frequency 1nF on TIMER1 and TIMER2 0.98 1.12 1.32 Hz. So approximately once per second the charging is stopped and the temperature is sensed.
At the time of product introduction Tantalum capacitors were commonly used for switching power supply designs. Today, large value ceramic capacitors are available and some customers choose to use these in designs. However, a ceramic capacitor has the ability to act as a "speaker" and I believe this is exactly what you are hearing in your design. There are many engineering articles and forum discussions related to this unwanted noise in ceramic capacitors (do a google search "ceramic capacitor piezo" and you will see).
The MAX1737/MAX1757/MAX1758 family are in my opinion some of the better truly standalone Li+ chargers with built in safety and cell qualification features. Unfortunately, the feature that stops the charger ever so briefly to take an accurate temperature measurement also lends itself to the "ticking" sound when using ceramics.
If you are hearing a slightly audible tick on the MAX1737 default evaluation kit circuit, then this is most likely normal. Of course I would expect the change to ceramic capacitors (C18, C19) to enhance this tick, and your tests seem to confirm this as well.
If you do the google search for "ceramic capacitor piezo" there are a number of results that also include methods for reducing the noise effects of ceramics. Placement of the ceramic capacitors on the board can affect the noise. Some ceramic capacitor manufacturers claim to have reduced piezo effect in certain product lines.