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No. The sentence is setting up a list consisting only of tricycle and bicycle and thus no comma is needed (because lists only need commas when there are three or more items.)
On the other hand, if you placed a comma after tricycle, you should also place a comma after bicycle to imply that "and a bicycle" is an added thought to the sentence.
If you really wanted to improve the sentence, you'd delete the "a" before bicycle to reinforce the list.
Thank you. I'm going with your suggestion about removing the "a". No commas anywhere as it is not my intent for the word bicycle to be an added thought to the sentence. It"s sort of a "concurrent" thought - if that makes any sense.