From the weights, the first coin appears to be a ¼ baht and the second coin 1 baht (=1 tical).
These types of coins are somewhat difficult to identify from the marks, but the second coin appears to have a mongkut and possibly a chakra symbol. It seems to me likely that this second coin is from the period of King Mongkut (Rama IV, 1851-1868 AD). It's similar, but not identical, to the coin listed for that period at
http://www.wangdermpalace.org/Pod%20Duang%20Money.html
There's also some general info at
https://coincoin.com/I112.htm
There are also listings for these coins in KM World Coins 1801-1900, but the photos are not very good or comprehensive. Still, I see a couple from Rama IV similar to your second coin.
Sorry I can't help more with the first coin.