Here Be Monsters Wiki

A Mama Creep Tree next to her 2-day and 1-day-old sapling (moved to be next to her)

Whether you like the appearance of Creep Trees, want the chance to get creeping ooze, or just like the challenge of spawning these relatively rare trees, it can be done.  

First of all, to spawn Creep Trees, you need to make sure that you have fewer than 40 wood-producing trees on your homestead. Fruit and blossom trees do not count.  Make sure there is enough space between your trees for another tree to grow. If they are too close, your saplings can spawn in another location on your homestead which will make it hard to identify your Mama Tree.

***Update*** Sometime in October 2013, the spawning locations became random on your homestead. If you don’t feel you are getting saplings of any type, check every hidden spot on your homestead and you might find tree babies hiding.

My What??

Each homestead that has wood trees will have a Mama Tree chosen by the game. It can be any wood-producing tree.  A Mama Tree isn't limited to only producing saplings of her type. A Banyan can spawn a Gingko. Or....a baby Creep Tree.  To identify your Mama Tree, keep an eye on those spaces between your adult wood trees. One day you will notice a tiny tree growing in a space. When this happens, the adult tree directly to the upper left of it  will most likely be your Mama Tree.  Move this baby tree if you wish to keep it. If not, chop it down and remove the stump.   Make sure not to plant flowers or put anything else in that space. You should get a new tree sapling every 24 hours.

Oh no!! I chopped down my Mama Tree!

Take a deep breath. It's ok. Did you remove the stump? If not, the tree will regrow. If you did, that's ok too. The game will assign Mama Tree status to another wood tree. If your Mama Tree is a creep  tree, and you want to chop her for ooze, go ahead but keep in mind she will take a longer time to regrow than the other tree types. Right now it seems to be roughly 6 days.  As long as you leave her stump though, she WILL still produce saplings.  

I only want Creep Trees!

If you get Creep Tree saplings, and decide all you want on your homestead are Creep Trees,  simply chop and remove all other wood-producing trees. This will greatly improve the chances that you will produce baby Creeps.  Wait to do this, however, until your Creep Trees are fully adults, so that one of them can act as a Mama Tree.  I have heard a couple of people say that their homestead doesn't produce saplings. I have not, however, been able to verify this so for now, I am going by what has been said on the official game forum, which is that each homestead will have a Mama Tree.  If yours doesn't I suggest filing a support ticket.