You can try, the downside is the electrical characteristic: tantalum is typically chosen, not for low ESR, but for modest and stable ESR.
For example, ceramic on that reset line, will probably resonate significantly when the button is pressed, triggering the logic IC's ESD diodes and potentially damaging it. A few ohms of added ESR dampens this.
The same admonishment goes for film capacitors.
Aluminum and tantalum, polymer and hybrid types, are available in a range of ESRs. Do not drop one in willy-nilly. Look for an appropriate ESR for replacement.
Timing capacitors can be replaced without much worry about ESR, as long as a stable value is used. Mind the three things which affect ceramic value: voltage, temperature and age. If you can't find characteristic graphs in the datasheet, don't buy it, keep shopping. It may seem unbelievable to worry about voltage change in a logic circuit, but that's how advanced ceramics are these days. Physically larger caps can be (but aren't guaranteed to be) better than small ones. Mind that leaded ceramics are nothing more than an SMT chip with leads attached, and dipped in epoxy; the size of the chip inside is what matters.
Tantalum shouldn't be failing in a timing application, so I would just as well recommend leaving those alone. Or if they are failed, replace them with the same type.
Tim