Android - Securing a young child's tablet
The overall outlook is not so great for you, AFAIK.
The Market has content filtering, check the Settings in the Market app.
For the browser, that's a wholly different kettle of fish. The built-in browser doesn't have any kind of filtering available. 3rd party browsers might, but they'll be trivial to sidestep (by simply opening the built-in browser).
The next best thing you can do is filter the tablets at the router, if it allows for that. However, that's only useful when they're at home (or other places where you can control their internet connection).
This isn't really manageable from a technical perspective (you could go some way towards it by sorting out your own firmware, using something like Cyanogen) as we often point out over on security.stackexchange.com once an attacker (in this case, your children) have a device, they control it.
So, my alternate course of action would be as detailed in this question over on parenting stackexchange - start off with visibility, using the devices together, and education - that will go much further towards making your children safe than any technical control you can implement.
What I have done with my 3 (now 5, 9 and 11) was let them use computers in the main room while we were there (aged 3 - 5) and then unsupervised until about 8 (but knowing we would be walking in and out) and over 8 year's old I trust them not to be stupid.
It helps that their dad is a security and privacy specialist who often provides awareness training in this area :-)
As I noted in your other thread, your best bet is probably to manually set a web proxy server via the devices network settings that filters by keyword or whitelists. Even if they do go to another person's house or try to get on another network, they will be unable to browse (especially if you are hosting the proxy server yourself on your own network; in that case, they most likely won't be able to browse to anything at all).
From wikipedia:
In computer networks, a proxy server is a server (a computer system or an application) that acts as an intermediary for requests from clients seeking resources from other servers. A client connects to the proxy server, requesting some service, such as a file, connection, web page, or other resource available from a different server. The proxy server evaluates the request according to its filtering rules. For example, it may filter traffic by IP address or protocol. If the request is validated by the filter, the proxy provides the resource by connecting to the relevant server and requesting the service on behalf of the client. A proxy server may optionally alter the client's request or the server's response, and sometimes it may serve the request without contacting the specified server. In this case, it 'caches' responses from the remote server, and returns subsequent requests for the same content directly.