Parents - If you are around the Marques Pombal area there is a playground for children close to the botanical garden in Park Eduardo VII. A huge pirate ship designed for 5+ but if younger children are there and properly watched, it's pleasant to have a coffee at the same time
Parents - If you are in Colombo Centre you can hire a little buggy car for the child. Also there's a section of the first floor dedicated to childrens' clothes and toys where several of the companies donated play equipment for the public area.
Parents -Bad weather- There's an amusement arcade on the top floor of Colombo Centre. The rules are that you need a swipe card to play any of the games or go on the rides. You go to the kiosk and with the money that you want to spend i.e. 3000esc (10 pounds) and the operator will take that money and give you the swipe card with a value of 3000esc. The games machines have labels as to how much it costs for one game. Even if you don't use all the credit that visit, you keep the card and can use it on the next visit. To recharge the card, either go back to the kiosk or use a machine. Have fun.
Parents - Monsanto - Get the No.2 or 13 to Monsanto park and as well as a nice day you'll also find Alto de Serafina (or Indian Park) as it may be known. A grand childrens play area which you will be hard pushed to get them away from. Open everyday 0900-2000 (summer) and 0900 to 1830 (winter).
As my pictures will show, you can also have a lot of fun at the oceanarium.
Like everywhere in Lisbon there's a lot of art and tiles also.